Tethered Satellite Research Articles

Along-track deployment control of space tether system for SAR-GMTI mission

Global, 24/7, and all-weather Synthetic Aperture Radars (SARs) are optimal platforms for Ground Moving Target Indication (GMTI) missions, and the tether constraint provides a stable mechanic connection for such configurations. To fulfill the requirements of such missions, the Space Tether System (STS) must be deployed to horizontal positions to form the necessary along-track interference baseline, which is unstable relative to traditional vertical positions and has not received adequate focus. To deal with this problem, this study focuses on the deployment control of the STS to the unstable horizontal positions. Firstly, the properties of the STS at the horizontal position are analyzed, and a synthetic criterion of measurement error is defined based on the observation principle of the GMTI mission. Secondly, two deployment control strategies are proposed, and corresponding desired trajectories are generated by considering two occasions respectively. In the end, considering the instability of horizontal positions, an adaptive closed-loop controller is designed utilizing the backstepping method to address gravitational moment and other disturbances. Simulations demonstrate that the system can successfully attain the desired horizontal positions under both deployment strategies, and the designed controller can quickly track trajectories under initial state errors and external disturbances.

Longitudinal vibrations and their suppression of a tethered satellite system using friction self-excitation mechanism

This paper proposes a friction self-excitation mechanism to regulate the longitudinal vibrations of the tether during the state-keeping phase of a two-body tethered satellite system. A simplified dynamic model is established, consisting of two mass blocks, a constant-length tether, and a conveyor belt. The Stribeck friction model is utilized to describe the effects of friction on the stability of longitudinal vibration. Numerical simulations reveal the instability phenomenon induced by Hopf bifurcation and indicate the potential self-excited vibration under different parameters. Additionally, the paper explores the design approach for the tether by introducing the concept of segmented tethering and its dynamic behavior under different design scenarios. Varying the stiffness of the tether can change the vibration modes of the system. Finally, a ground experiment is carried out to evaluate the dynamic behaviors of the system and to demonstrate the effectiveness of the proposed vibration suppression mechanism.

Space tether research at the University of Stuttgart

Space tether research activities at the University date back to the 1990s. First research projects investigated tether-assisted re-entry of payload return capsules from space stations. Tether research was resumed in 2015 focusing on the application of tethered planetary exploration rovers, based on the micro-rover Nanokhod. This includes robust, highly-integrated and miniaturised tethers and tether spooling systems, which are specifically adapted to the challenging lunar environmental and dust conditions. For this, several prototypes were developed and tested and a tether-dust testing facility was setup. In addition, developments have been made in the tether detection by creating a simulation framework, tracking algorithms and low-fidelity test bench for the verification of the algorithms. Based on the experience of the planetary tether applications, the research at the University of Stuttgart was expanded to Tethered Satellite Systems in 2022, utilising the tether spooling technology. In-depth studies on tethered CubeSat missions were developed together with students as part of educational activities, including tethered rendezvous capabilities and electrodynamic tether operation. In addition, breadboard models of optical detection and tracking payloads were developed for tracking a CubeSat sized object at full tether deployment of 100m. Additional subsystem development is currently in progress, consolidating the results of the mission studies, as well as dynamic analyses and simulations of the tethered satellite system. Concurrently, a third tether application research area was established, looking into studies for creating tether-based spaceflight infrastructure for lunar exploration missions. A concept study of a Momentum Exchange Tether system to transfer large payloads from Low Earth Orbit to a lunar transfer orbit was conducted and feasible tether system configurations were drafted. Various technological and operational challenges were identified and are now the focus of ongoing Momentum Exchange Tether research at the University of Stuttgart.

Deployment Dynamics and Control of a Hub-Spoke Tethered Satellite Formation Using Combined Arbitrary Lagrange-Euler and Referenced Nodal Coordinate Formulation

Abstract A novel modeling framework combining arbitrary Lagrange-Euler and referenced nodal coordinate formulation (ALE-RNCF) is proposed for deployment dynamics and control of a hub-spoke tethered satellite formation. The ALE-RNCF approach allows for an accurate analysis of the intricate coupling effect between the orbit, attitude, and deployment dynamics, and its strengths lie in overcoming the accuracy loss and low-efficiency issues when dealing with spatial and temporal multiscale problems. Specifically, the orbital and attitude motions are separated with vibrations of the variable-length ALE tethers through the RNCF, which is the main distinguishing feature over the widely-used absolute nodal coordinate formulation. To achieve stable deployment, the control torque is added to the central satellite by employing the proportional-differential algorithm, where the maximum tension of tethers or the spinning angular velocity is selected as the control object. Various cases with different deployment velocities, target tensions, and orbital heights are simulated and corresponding effects on the deployment performance are analyzed. The proposed ALE-RNCF approach provides a comprehensive understanding of the orbit-attitude-structure coupled behavior during the deployment of the hub-spoke tethered satellite formation and contributes to the development of effective control strategies.

Nonlinear dynamic modeling and vibration analysis for flexible tethered satellite systems under large deformations

The escalating threat posed by space debris necessitates innovative approaches for its removal. This article presents a comprehensive mathematical modeling and dynamic analysis of a flexible tethered satellite system (FTSS) in the post-capture phase, taking into account nonlinear strain effects for the flexible appendages. The FTSS consists of a rigid central body satellite, two identical flexible panels, and a towing mass that manipulates the satellite through a tether. We develop a detailed dynamic model that accurately represents the system’s three-dimensional motion, incorporating the rigid body’s 6 degrees of freedom (DOF), the tether’s 3 DOF motion, and two modal generalized coordinates for each panel. The extended Hamilton method is employed to derive this model, enabling us to investigate the conditions under which nonlinear strain considerations become critical. The findings of this article reveal that nonlinear strain effects can profoundly impact the system’s dynamics under certain geometric and forcing conditions, often overlooked in previous studies. In these scenarios, the panel strains exceed the linear regime, necessitating the use of nonlinear models for accurate representation. This work emphasizes the importance of incorporating nonlinear strain terms in the dynamic analysis of FTSSs, particularly when dealing with large deformations and high-amplitude vibrations encountered in debris removal applications.

Dynamic analysis of the tethered satellite system considering uncertain but bounded parameters

Dynamic analysis of the tethered satellite system (TSS) can provide a fundamental guideline to the evaluation of performance and robust design of the system examined. Uncertainties inherited with the parameters would induce unexpected variation of the response and deteriorate the reliability of the system. In this work, the effect of uncertain mass of the satellites on the deployment and retrieval dynamics of the TSS is investigated. First the interval mode is employed to take the variation of mass of satellite into account in the processes of deployment and retrieval. Then, the Chebyshev interval method is used to obtain the lower and upper response bounds of the TSS. To achieve a smooth and reliable implementation of deployment and retrieval, the nonlinear programming based on the Gauss pseudo-spectral method is adopted to obtain optimal trajectory of tether velocity. Numerical results show that the uncertainties of mass of the satellites have a distinct influence on the response of tether tension in the processes of deployment and retrieval.

Message from the Guest Editors of the Special Issue on Tethered Satellite System

Message from the Guest Editors of the Special Issue on Tethered Satellite System

A distributed space radar sounder using a cross-track flying tethered satellite system

The objective of this paper is to analyze the performance of two possible architectures of tethered satellite systems, used as a platform for a distributed radar sounder. The first architecture consists in a cross-track oriented tethered satellite system, controlled and stabilized by exploiting the aerodynamic forces generated by the interaction with the rarefied atmosphere in Low Earth Orbit. The second architecture involves a tethered satellite system controlled through gyroscopic stabilization, obtained by spinning the system about an axis contained in the orbital plane. After a brief survey of radar sounding techniques, the methodology is introduced for describing the geometry of the systems and their characteristics, the performance of the two architectures are then compared with each other and with the current state of the art. By analyzing the modeled nominal behavior, it is shown that the two proposed architectures can achieve continuous or multiple observations, respectively, at maximum cross-track resolution, during one orbit, minimizing clutter noise. This is a considerable improvement of performance versus a formation flight architecture which can typically achieve only up to four observations per orbit. Finally, the advantages and disadvantages of each architecture are studied, and their possible mission scenarios are discussed.

On the optimality of uniform velocity–deceleration separation scheme for tethered satellite systems

On the optimality of uniform velocity–deceleration separation scheme for tethered satellite systems

Characterization of out-of-plane libration of tethered satellite systems in elliptical orbits

This paper investigates the dynamic behavior of a tethered satellite system in an elliptical orbit as the tethered subsatellite is deployed from a mother satellite at an out-of-plane angle while maintaining the tether at a constant in-plane pitch angle by a predefined control force acting on the subsatellite. A variable-length pendulum model is employed to describe the purely out-of-plane tether deployment dynamics, from which an analytical tether deployment control law is derived. The stability condition of the analytical control law is examined by Floquet theory. The corresponding analytical deployment law is asymptotically stable, and the requirement for a positive tension control input is guaranteed to ensure the controllability of the tether system. Following deployment, the critical conditions for the out-of-plane libration of the tethered subsatellite to become chaotic during the station-keeping phase are examined. Finally, simulation results reveal that the proposed approach can effectively and rapidly identify periodic, quasiperiodic, and chaotic motions using bifurcation diagrams, which provides valuable insights for enhancing the stability and reliability of such tethered satellite systems.

Model and Dynamic Analysis of a Three-Body Tethered Satellite System in Three Dimensions

The three-body tethered satellite system is a new potential technology for the purposes of orbital transportation. In contrast to conventional orbit transfer methods, this system is expected to transport space supplies to a predetermined orbital altitude without consuming fuel; however, the unwanted libration resulting from the Coriolis force acting on moving subsatellites may induce tumbling within the system. In order to analyze the strongly coupled characteristics of the libration motion and the variable-length tethers, a six-DOF dynamic model of the system based on Newton’s law is established. By utilizing the dynamic equations and stability criterion for linear systems, three equilibrium configurations of the satellite system with two constant-length tethers are given. The coupling characteristics of the libration angles are analyzed based on mechanical features and simulations. The results demonstrate that part of the libration energy can transfer from out-of-plane motion to in-plane motion during out-of-plane libration, but not vice versa or when in-plane libration occurs alone. Furthermore, the dynamic characteristic of this system with a predesigned deployment strategy is surveyed. This investigation reveals that such a strategy can rapidly suppress the out-of-plane libration motion while maintaining purely sinusoidal oscillations in the in-plane motion.

Adaptive neural dynamic-based hybrid control strategy for stable retrieval of tethered satellite systems

Adaptive neural dynamic-based hybrid control strategy for stable retrieval of tethered satellite systems

Fault-Tolerant Fuzzy-Resilient Control for Fractional-Order Stochastic Underactuated System With Unmodeled Dynamics and Actuator Saturation.

This article is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order α ∈ (0,1) . First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and It∧ o differential formulation to design proper multiple Lyapunov-Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

Data-driven optimal controller design for sub-satellite deployment of tethered satellite system

<abstract><p>In the paper, we presented a data-driven optimal control method for the sub-satellite deployment of tethered satellite systems during the release phase, with the objective of reducing the libration angle fluctuation during system work. First, the dynamic equation of the tethered satellite system was established and processed dimensionless. Considering the presence of noise when sensors were put on the satellite to measure the libration angle, the corresponding state equation was derived. Next, we estimated the system state using an unscented Kalman filter and established a performance index and the Hamilton function. Based on the index, we designed an optimal control strategy and provided sufficient conditions for the asymptotic stability of the closed-loop system. We used critic-actor neural networks based on measurement data to implement the data-driven control algorithm to approximate the performance index function and the control policy, respectively. Finally, taking a tethered satellite system as an example, a simulation showed that the unscented Kalman filter can effectively estimate the system state and improve the impact of noise on the system, and the proposed optimal control strategy ensured that the tethered satellite system is stable, which shows the applicability and effectiveness of the control strategy in reducing the tether vibration of the disturbed system.</p></abstract>

The effects of deployment friction on the dynamics of nonconductive space tethers

At present, the neglect of deployment friction could lead to a significant deviation in the numerical results from the real deployment dynamic characteristics of the nonconductive space tether. To solve this problem, a dedicated experimental setup for tether deployment was firstly employed to measure the deployment friction of nonconductive space tether, the dependences of the deployment friction on the tether diameter, deployment velocity and deployment angle (which is the angle between the deployment direction and the normal direction of the tether exit) were determined. The effect of deployment parameters on the dynamics in both the uncontrolled tether deployment and the station-keeping stages were evaluated based on the “dumbbell” and “extended dumbbell” models, the measured deployment frictions was applied to the models. The numerical results show that the uncontrolled nonconductive tether deployment is great limited by the deployment friction; the tether deployment capability and dynamic stability could be enhanced by increasing the initial deployment velocity (≤2 m/s) and satellite effective mass, as well as decreasing the orbital altitude. To guarantee maximum tether deployment capability and dynamic stability, an optimal matching relationship between the tether full length and satellite total mass is given, which is of substantial importance for the uncontrolled deployment process of the nonconductive space tether system at the design stage.

Detumbling of Underactuated Tethered Satellite System Based on Hierarchical Sliding Mode Control

Millions of space debris pose a significant risk to operational spacecraft, making active debris removal (ADR) missions an urgent priority. Net capturing is a promising method to remove space debris objects due to its multiple advantages. However, once a target has been captured, a combined tethered system comprising the chaser, the target, and the tethers is formed, which requires effective stabilization. In this paper, stabilization of the entire postcapture system is realized by solely controlling the active chaser satellite. Such a control strategy can attenuate system hardware facilities compared with those by applying additional tether control such as using a winding mechanism, which were mostly discussed in the literature. Further, for the first time, considering the uncertainties during the capture process, including inaccurate target parameters, initial attitude error of the target, and external disturbances, a hierarchical sliding mode controller (HSMC) with two sublayers is developed to detumble this underactuated system. Additionally, a hybrid position controller is proposed to eliminate the undesired swing motion within the system. Numerical simulations demonstrate that HSMC method delivers better performance over the proportional-derivative controller in efficiency and robustness for postcapture stabilization of the combined tethered system. Overall, our proposed control strategy offers a promising solution for future ADR missions, contributing to a safer and more sustainable space environment.

Proportional-derivative Control of Second-order Tethered Satellites System Based on Extended State Observer and Feed-forward Compensation

This paper researches the proportional-derivative (PD) feedback control with feed-forward compensations from input for a triangular tethered satellite system (TTSS), and the extended state observer (ESO) design which is further incorporated in control to estimate the structural uncertainties in system. By expanding Lagrangian equations under chosen variables, the dynamic equations of TTSS are derived which is the second-order nonlinear equation. Then the feedback control under typical feed-forward compensations is discussed as the nonlinear functions in system are counteracted, and the controlled outputs are computed by deriving the transfer functions of the transformed structures. Moreover, in case of the uncertain structures in system which may constrain the control effect, ESO-based PD control is further proposed, and the observed error and controlled accuracy are analyzed by Lyapunov functions. Simulation results on the designed controls are presented to validate the theoretic analyses.

Digital deployment control of a tethered satellite system with constrained tension

This paper investigates the dynamics and digital control issues of deploying a tethered satellite using constrained tether tension. To cater to the requirements of the digital techniques applied in engineering applications, unlike existing results, this study develops a digital feedback control strategy to achieve the rapid and stable tether deployment. The proposed digital control law consists of discretized and quantized tether states and is derived based on continuous-time dynamical model instead of the discrete-time one. To keep tether tension at a positive value when implementing control action, the constraint on tether tension is explicitly accounted for during controller design. Furthermore, the discretization and quantization errors are treated as the uncertain terms in the closed-loop system which can be handled by robust analysis and synthesis techniques. A Lyapunov functional, together with an integral performance index, is made to prove the stability of the system, and the desired controller is obtained by solving an optimization problem. Finally, the effectiveness of the proposed controller is demonstrated by numerical simulation.

Koopman Operator-Based Data-Driven Identification of Tethered Subsatellite Deployment Dynamics

Compact tether-based actuation is a suitable approach for the deployment of femto/picosatellite bodies from CubeSats using ultrasmall electrodynamic tethers for fuel-free propulsion and deorbiting. Despite the advantages of tethered satellite systems, control technologies for these have yet to mature in several domains including robustness to structural faults and unmodeled dynamics. A proposed solution for the identification of disturbances to tethered satellite dynamics is to use a data-driven algorithm to learn the system’s behavior over previous orbits and then provide an estimated prediction for the evolution of system states. To achieve the goal of state prediction via a globally linearized system model, this paper employs the Koopman operator constructed from observed dynamics to extrapolate future motion of a tethered subsatellite subject to unknown disturbances while being deployed from its mothership. Numerical simulations of the constructed model versus the nonlinear model of the tethered satellite system demonstrate the effective prediction capabilities of the proposed Koopman operator-based numerical algorithm for the general flight characteristics many orbits into the future.

Event-model-based fuzzy sliding mode deployment control for triangular tethered satellite systems suffering external disturbance

This paper researches the deployment control problem of the space triangular tethered satellite system under external disturbances and communication constraints from sensor to controller. An adaptive model-based event-triggered fuzzy sliding mode control scheme is proposed, making sure that the system is deployed to the specified configuration. The disturbance observer is used to estimate external disturbances, while the estimated model is constructed at the controller side to update control input without interruption under event-triggered mechanism. Then, the event-triggered fuzzy sliding mode controller based on the estimated model is designed, ensuring that the communication burden is greatly reduced and precise deployment control is achieved. Further, the stability of the closed-loop system is proved by the Lyapunov function based on the hybrid dynamical system. Eventually, the effectiveness of the proposed control scheme is tested by simulation tests.