This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel an...This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only.The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS.To enhance the robustness of the proposed controller,multiple perturbations of the orbital dynamics,modeling uncertainties,and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously,such that these perturbations are well compensated for during the control design of the EDTS.Furthermore,a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law.The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory.Finally,numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.展开更多
In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close...In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close.First of all,to perform its geometrically nonlinear deformation,discrete different geometry theory is applied to model the mechanical response of a flexible net.Based on the discretization of the whole structure into multiple vertexes and lines,the internal force and associated Hession are derived in a closed form to solve a series of nonlinear dynamic equations of motion.The spread and deployment of a packaged net can be realized using this well-established net solver.Next,a multidimensional incremental potential formulation is selected to achieve the intersection-free boundary nonlinear contact and collision between the deformable net and rigid debris.Finally,for the closing mechanism analysis,a log-like barrier functional is derived to achieve the nondeviation condition between the ring–rod linkage system.The C2 continuous log barrier functionals constructed for both the contact model and the linkage system are smooth and differentiable,and,therefore,the nonlinear net capture dynamic system can be efficiently solved through a fully implicit time integrator.Overall,as a demonstration,the whole capture process of a defunct satellite using a hexagon net is simulated through our well-established numerical framework.We believe that our comprehensive numerical methods could provide new insight into the optimal design of active debris removal systems and promote further development of the online control of tether tugging systems.展开更多
The space debris occupies the orbit resources greatly,which seriously threats the safety of spacecraft for its high risks of collisions.Many theories about space debris removal have been put forward in recent years.Th...The space debris occupies the orbit resources greatly,which seriously threats the safety of spacecraft for its high risks of collisions.Many theories about space debris removal have been put forward in recent years.The Electro Dynamic Tether(EDT),which can be deployed under gravity gradient,is considered to be an effective method to remove debris in low orbit for its low power consumption.However,in order to generate sufficient Lorentz force,the EDT needs to be deployed to several kilometers,which increases the risks of tangling and the instability of the EDT system.In the deployment process,different initial in-plane/out-of-plane angles,caused by direction error at initial release or the initial selection of ejection,affect the motion of EDT system seriously.In order to solve these problems,firstly,this paper establishes the dynamic model of the EDT system.Then,based on the model,safety metrics of avoiding tangling and assessing system stability during EDT deployment stage are designed to quantitatively evaluate the EDT system security.Finally,several numerical simulations are established to determine the safety ranges of the initial in-plane/out-of-plane angles on the EDT deployment.展开更多
The libration control problem of space tether system(STS)for post-capture of payload is studied.The process of payload capture will cause tether swing and deviation from the nominal position,resulting in the failure o...The libration control problem of space tether system(STS)for post-capture of payload is studied.The process of payload capture will cause tether swing and deviation from the nominal position,resulting in the failure of capture mission.Due to unknown inertial parameters after capturing the payload,an adaptive optimal control based on policy iteration is developed to stabilize the uncertain dynamic system in the post-capture phase.By introducing integral reinforcement learning(IRL)scheme,the algebraic Riccati equation(ARE)can be online solved without known dynamics.To avoid computational burden from iteration equations,the online implementation of policy iteration algorithm is provided by the least-squares solution method.Finally,the effectiveness of the algorithm is validated by numerical simulations.展开更多
A new flexible tether-net space robotic system used to capture space debris is presented in this paper. With a mass point assumption, a dynamic model of the tether-net system was established in orbital frame by applyi...A new flexible tether-net space robotic system used to capture space debris is presented in this paper. With a mass point assumption, a dynamic model of the tether-net system was established in orbital frame by applying Lagrange Equations. In order to investigate the net in-plane trajectories after being cast, the non-controlled R-bar and V-bar captures were simulated with ignoring the out-of-plane libration, and the effect of in-plane libration on the trajectories of the capture net was demonstrated by simulation results. With an effort to damp the in-plane libration, the control scheme based on tether tension was investigated, then an integrated control scheme was proposed by introducing thrusters into the system, and the nonlinear close-loop dynamics was linearised by feedforward strategy. Simulation results show that the feedforward controller is effective for in-plane libration damping and enables the capture net to track an expected trajectory.展开更多
A high‐fidelity multibody‐system dynamic model of the looped tether transportation system(L‐TTS)is proposed in this study to study its large deformation as well as large overall motion.The absolute nodal coordinate...A high‐fidelity multibody‐system dynamic model of the looped tether transportation system(L‐TTS)is proposed in this study to study its large deformation as well as large overall motion.The absolute nodal coordinate formulation(ANCF)‐based gradient‐deficient beam element is employed to establish the accurate model of the two flexible tethers subject to large deformations.The relative movement of climbers along tethers is described by using the sliding joint model based on ANCF.To reduce the collision risks between tethers and climbers,two libration suppression strategies,namely,the decelerated motion of climbers relative to tethers and multiple climbers per tether are investigated in this study.Several numerical simulations not only validate the effectiveness of the two strategies in reducing the collision risks between climbers and tethers,the overall librations of L‐TTS,and the magnitudes of the longitudinal elastic force of tethers,but also verify the good performance of the high‐fidelity model proposed in this study for dynamic simulation of the L‐TTS in microgravity conditions.展开更多
The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and...The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.展开更多
The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital ...The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11902145 and 12232011China Postdoctoral Science Foundation under Grant No.2021M691574Fundamental Research Funds for the Central Universities under Grant No.NS2022002.
文摘This study focuses on stabilizing the libration dynamics of an electrodynamic tether system(EDTS)using generalized torques induced by the Lorentz force.In contrast to existing numerical optimization methods,a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only.The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS.To enhance the robustness of the proposed controller,multiple perturbations of the orbital dynamics,modeling uncertainties,and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously,such that these perturbations are well compensated for during the control design of the EDTS.Furthermore,a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law.The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory.Finally,numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law.
基金Natural Science Foundation of Jiangsu Province,China,Grant/Award Number:BK20220794。
文摘In this paper,we develop an exhaustive numerical simulator for the dynamic visualization and behavior prediction of the tether-net system during the whole space debris capture phases,including spread,contact,and close.First of all,to perform its geometrically nonlinear deformation,discrete different geometry theory is applied to model the mechanical response of a flexible net.Based on the discretization of the whole structure into multiple vertexes and lines,the internal force and associated Hession are derived in a closed form to solve a series of nonlinear dynamic equations of motion.The spread and deployment of a packaged net can be realized using this well-established net solver.Next,a multidimensional incremental potential formulation is selected to achieve the intersection-free boundary nonlinear contact and collision between the deformable net and rigid debris.Finally,for the closing mechanism analysis,a log-like barrier functional is derived to achieve the nondeviation condition between the ring–rod linkage system.The C2 continuous log barrier functionals constructed for both the contact model and the linkage system are smooth and differentiable,and,therefore,the nonlinear net capture dynamic system can be efficiently solved through a fully implicit time integrator.Overall,as a demonstration,the whole capture process of a defunct satellite using a hexagon net is simulated through our well-established numerical framework.We believe that our comprehensive numerical methods could provide new insight into the optimal design of active debris removal systems and promote further development of the online control of tether tugging systems.
基金co-supported by the National Natural Science Foundation of China(Nos.51975021,U1913206)。
文摘The space debris occupies the orbit resources greatly,which seriously threats the safety of spacecraft for its high risks of collisions.Many theories about space debris removal have been put forward in recent years.The Electro Dynamic Tether(EDT),which can be deployed under gravity gradient,is considered to be an effective method to remove debris in low orbit for its low power consumption.However,in order to generate sufficient Lorentz force,the EDT needs to be deployed to several kilometers,which increases the risks of tangling and the instability of the EDT system.In the deployment process,different initial in-plane/out-of-plane angles,caused by direction error at initial release or the initial selection of ejection,affect the motion of EDT system seriously.In order to solve these problems,firstly,this paper establishes the dynamic model of the EDT system.Then,based on the model,safety metrics of avoiding tangling and assessing system stability during EDT deployment stage are designed to quantitatively evaluate the EDT system security.Finally,several numerical simulations are established to determine the safety ranges of the initial in-plane/out-of-plane angles on the EDT deployment.
基金supported by the National Natural Science Foundation of China(No.62111530051)the Fundamental Research Funds for the Central Universities(No.3102017JC06002)the Shaanxi Science and Technology Program,China(No.2017KW-ZD-04).
文摘The libration control problem of space tether system(STS)for post-capture of payload is studied.The process of payload capture will cause tether swing and deviation from the nominal position,resulting in the failure of capture mission.Due to unknown inertial parameters after capturing the payload,an adaptive optimal control based on policy iteration is developed to stabilize the uncertain dynamic system in the post-capture phase.By introducing integral reinforcement learning(IRL)scheme,the algebraic Riccati equation(ARE)can be online solved without known dynamics.To avoid computational burden from iteration equations,the online implementation of policy iteration algorithm is provided by the least-squares solution method.Finally,the effectiveness of the algorithm is validated by numerical simulations.
基金Sponsored by the High Technology Research & Development Program of China(Grant No.2002AA742012)
文摘A new flexible tether-net space robotic system used to capture space debris is presented in this paper. With a mass point assumption, a dynamic model of the tether-net system was established in orbital frame by applying Lagrange Equations. In order to investigate the net in-plane trajectories after being cast, the non-controlled R-bar and V-bar captures were simulated with ignoring the out-of-plane libration, and the effect of in-plane libration on the trajectories of the capture net was demonstrated by simulation results. With an effort to damp the in-plane libration, the control scheme based on tether tension was investigated, then an integrated control scheme was proposed by introducing thrusters into the system, and the nonlinear close-loop dynamics was linearised by feedforward strategy. Simulation results show that the feedforward controller is effective for in-plane libration damping and enables the capture net to track an expected trajectory.
基金This study was supported in part by the National Natural Science Foundation of China(Grant No.11902159)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20190390)It was also supported in part by the China Postdoctoral Science Foundation(Grant No.2019M661849).
文摘A high‐fidelity multibody‐system dynamic model of the looped tether transportation system(L‐TTS)is proposed in this study to study its large deformation as well as large overall motion.The absolute nodal coordinate formulation(ANCF)‐based gradient‐deficient beam element is employed to establish the accurate model of the two flexible tethers subject to large deformations.The relative movement of climbers along tethers is described by using the sliding joint model based on ANCF.To reduce the collision risks between tethers and climbers,two libration suppression strategies,namely,the decelerated motion of climbers relative to tethers and multiple climbers per tether are investigated in this study.Several numerical simulations not only validate the effectiveness of the two strategies in reducing the collision risks between climbers and tethers,the overall librations of L‐TTS,and the magnitudes of the longitudinal elastic force of tethers,but also verify the good performance of the high‐fidelity model proposed in this study for dynamic simulation of the L‐TTS in microgravity conditions.
基金the National Natural Science Foundation of China(10672073)the Innovation Fund for Graduate Students,Nanjing University of Aeronautics and Astronautics
文摘The concept of tethered satellite system （TSS） promises to revolutionize many aspects of space exploration and exploitation. It provides not only numerous possible and valuable applications, but also challenging and interesting problems related to their dynamics, control, and physical implementation. Over the past decades, this exciting topic has attracted significant attention from many researchers and gained a vast number of analytical, numerical and experimental achievements with a focus on the two essential aspects of both dynamics and control. This review article presents the historic background and recent hot topics for the space tethers, and introduces the dynamics and control of TSSs in a progressive manner, from basic operating principles to the state-of-the-art achievements.
基金supported by the National Natural Science Foundation of China(Nos.11002068 and11202094)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(No.0113Y01)the Priority Academic Program of Jiangsu Higher Education Institutions
文摘The paper studies the nonlinear dynamics of a flexible tethered satellite system subject to space environments, such as the J2 perturbation, the air drag force, the solar pressure, the heating effect, and the orbital eccentricity. The flexible tether is modeled as a series of lumped masses and viscoelastic dampers so that a finite multi- degree-of-freedom nonlinear system is obtained. The stability of equilibrium positions of the nonlinear system is then analyzed via a simplified two-degree-freedom model in an orbital reference frame. In-plane motions of the tethered satellite system are studied numerically, taking the space environments into account. A large number of numerical simulations show that the flexible tethered satellite system displays nonlinear dynamic characteristics, such as bifurcations, quasi-periodic oscillations, and chaotic motions.
