In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions betwee...In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.展开更多
This paper presents Part II of a review on DFACS,which specifically focuses on the modeling and analysis of disturbances and noises in DFACSs.In Part I,the system composition and dynamics model of the DFACS were prese...This paper presents Part II of a review on DFACS,which specifically focuses on the modeling and analysis of disturbances and noises in DFACSs.In Part I,the system composition and dynamics model of the DFACS were presented.In this paper,we discuss the effects of disturbance forces and noises on the system,and summarize various analysis and modeling methods for these interferences,including the integral method,frequency domain analysis method,and magnitude evaluation method.By analyzing the impact of disturbances and noises on the system,the paper also summarizes the system’s performance under slight interferences.Additionally,we highlight current research difficulties in the field of DFACS noise analysis.Overall,this paper provides valuable insights into the modeling and analysis of disturbances and noises in DFACSs,and identifies key areas for future research.展开更多
This study investigates the orbital Target-Attacker-Defender(TAD)game problem in the context of space missions.In this game,the Attacker and the Defender compete for a Target that is unable to maneuver due to its orig...This study investigates the orbital Target-Attacker-Defender(TAD)game problem in the context of space missions.In this game,the Attacker and the Defender compete for a Target that is unable to maneuver due to its original mission constraints.This paper establishes three TAD game models based on the thrust output capabilities:unconstrained thrust output,thrust constrained by an upper bound,and fixed thrust magnitude.These models are then solved using differential game theory to obtain Nash equilibrium solutions for the game problems,and the correctness and effectiveness of the solution methods are verified through simulations.Furthermore,an analysis of the winning mechanisms of the game is conducted,identifying key factors that influence the game’s outcomes,including weight coefficients in payoffs,the maximum thrust acceleration limit,and the initial game state.Considering the unique characteristics of space missions,a specific focus is given to the analysis of the Defender’s initial states in the hovering formation and in-plane circling formation,revealing overall success patterns for defense strategies from these two formations.In summary,this study provides valuable insights into the control strategies and winning mechanisms of orbital TAD games,deepening our understanding of these games and offering practical guidance to improve success rates in real-world scenarios.展开更多
The Drag-Free and Attitude Control System(DFACS)is a critical platform for various space missions,including high precision satellite navigation,geoscience and gravity field measurement,and space scientific experiments...The Drag-Free and Attitude Control System(DFACS)is a critical platform for various space missions,including high precision satellite navigation,geoscience and gravity field measurement,and space scientific experiments.This paper presents a comprehensive review of over sixty years of research on the design and dynamics model of DFACS.Firstly,we examine the open literature on DFACS and its applications in Drag-Free missions,providing readers with necessary background information on the field.Secondly,we analyze the system configurations and main characteristics of different DFACSs,paying particular attention to the coupling mechanism between the system configuration and dynamics model.Thirdly,we summarize the dynamics modeling methods and main dynamics models of DFACS from multiple perspectives,including common fundamentals and specific applications.Lastly,we identify current challenges and technological difficulties in the system design and dynamics modeling of DFACS,while suggesting potential avenues for future research.This paper aims to provide readers with a comprehensive understanding of the state-of-the-art in DFACS research,as well as the future prospects and challenges in this field.展开更多
This study proposes a parametric formation control method for the cooperative observation of the China Space Station(CSS)using multiple nanosatellites.First,a simplified geometrical model of the CSS is constructed usi...This study proposes a parametric formation control method for the cooperative observation of the China Space Station(CSS)using multiple nanosatellites.First,a simplified geometrical model of the CSS is constructed using fundamental solids,such as the capsule body and cuboid.Second,the spacecraft formation configuration for the observation mission is characterized by a three-dimensional(3D)Lissajous curve using related design parameters under the full-coverage observation requirements of specific parts,such as the CSS connecting section and collision avoidance constraints.Third,a double-layer control law is designed for each nanosatellite,in which the upper layer is a distributed observer for recognizing the target formation configuration parameters,and the lower layer is a trajectory-tracking controller to make the nanosatellite converge to its temporary target position calculated from the upper layer’s outputs.The closed-loop control stability is proven under the condition that the communication network topology of the nanosatellite cluster contains a directed spanning tree.Finally,the control method is verified by numerical simulation,where the CSS connecting section is selected as the observation target,and ten small nanosatellites are assumed to perform the cooperative observation mission.The simulation results demonstrate that the double-layer control law is robust to single-point communication failures and suitable for the accompanying missions of large space objects with multiple nanosatellites.展开更多
This paper discusses the modeling and solving of orbital pursuit-evasion games(OPEGs)under J_(2)perturbation.The optimal long-range maneuver method under J_(2)perturbation is designed,and it is proved that the effect ...This paper discusses the modeling and solving of orbital pursuit-evasion games(OPEGs)under J_(2)perturbation.The optimal long-range maneuver method under J_(2)perturbation is designed,and it is proved that the effect of eccentricity can be ignored when transfer times and theΔV budgets are fixed.It is discovered that when the inclination between the initial and target orbit is equal and is between 10°and 25°,the whole maneuver process can be simplified to a fixed-inclination transfer.Subsequently,a long-term OPEG model is provided under the assumption of fixed inclination,zero eccentricity,and impulsive thrust.Winning conditions of OPEGs under J_(2)perturbation are then carefully derived,with long-time OPEG(J_(2)dominated)and short-time OPEG(traditional)separated,and typical tactics of both sides formulated and verified.These studies are further extended to the“Arrival time matching game”for maintaining/avoiding resonant arrival time under J_(2)perturbation,and the advantages and disadvantages of both sides are analyzed.The models and strategies obtained in this paper can be potentially used in practical applications of OPEGs,especially for evaders that have low thrust-weight ratios and are weak in traditional short-term OPEGs.展开更多
This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two sate...This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two satellites is firstly proposed through a detailed analysis of the relative orbital dynamics.It is proved that the existing periodic solutions of satellite relative motion such as in-plane 2:1 elliptic and circular periodic relative orbits both belong to the ellipsoid family of periodic relative orbits.The motion planes and their locations and orientations of the general periodic relative orbits are then determined as the analytic functions of the initial relative states.The maximal and minimal distances from the relative orbit to the origin are further analytically calculated too.A formation design algorithm is then proposed for optimal observation of feature points of the target considering various requirements of collision avoidance and observable distance by using this parametric model.Numerical examples about target inspection are introduced to quantitively evaluate and verify the models and methods.The simulation results are well consistent with the theoretical predictions,showing that the design proposed can be potentially applied for future practical on-orbit service missions.展开更多
This paper explores the blocking capabilities of a spacecraft deployed near Earth-Moon L1 libration point against another spacecraft attempting lunar gravity assist,based on theΔV required for interception.The study ...This paper explores the blocking capabilities of a spacecraft deployed near Earth-Moon L1 libration point against another spacecraft attempting lunar gravity assist,based on theΔV required for interception.The study demonstrates that a pursuer at L1 libration point can effectively block low-energy evaders with minimalΔV expenditure,creating a blockade against their use of gravity assists.However,blocking against high-energy evaders is relatively weaker.Pursuers on Lyapunov orbits can execute blockades that L1 pursuers cannot,albeit with lower mission-capable rates.The paper discusses mission-capable rates for different Lyapunov orbits and evader energies,revealing that each Lyapunov orbit has its unique optimal blocking energy,decreasing as the Lyapunov orbit size expands.In addition,the paper proposes a strategy for evaders to bypass blockades by sacrificing a portion of theirΔV and verifies it numerically.The analysis covers the cost and benefits of the L1 libration point-related blockade,the importance of the mission-capable rate,and the possibility of lunar-orbit blocking.These findings provide insights for future research on orbital games in the Earth-Moon system and orbital blockade.展开更多
A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rota...A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.展开更多
基金supported by National Natural Science Foundation of China(No.12172288)National Key Basic Research Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601 and 2021YFC2202603)General Program of Natural Science Foundation of Higher Education of Jiangsu Province(No.21KJB590001)。
文摘In this paper,minimum-fuel rendezvous is investigated for the case in which the reference orbit is highly elliptic.To this end,the well-known Tschauner-Hempel equations are used to describe the relative motions between rendezvous spacecraft and the target.Lawden’s primer vector theory is then applied on this linear but time-varying system.The analytical solution of the required primer vector for this problem is then derived by using a recently developed method.For the existing non-optimal solutions which don’t satisfy the conditions,the methods are further designed to improve the performance by shifting impulses or adding a new one.Finally,two algorithms are developed for free-impulse time-fixed rendezvous problems.The first algorithm can determine the globally optimal trajectory with the optimal number of impulses.The second one enables for fast trajectory planning.The proposed algorithms have been successfully applied to coplanar and three-dimensional rendezvous problems in which the target is flying on highly elliptical orbits.
基金This research was supported by National Key R&D Program of China:Gravitational Wave Detection Project(Nos.2021YFC2202601,2021YFC2202603)National Natural Science Foundation of China(No.12172288).
文摘This paper presents Part II of a review on DFACS,which specifically focuses on the modeling and analysis of disturbances and noises in DFACSs.In Part I,the system composition and dynamics model of the DFACS were presented.In this paper,we discuss the effects of disturbance forces and noises on the system,and summarize various analysis and modeling methods for these interferences,including the integral method,frequency domain analysis method,and magnitude evaluation method.By analyzing the impact of disturbances and noises on the system,the paper also summarizes the system’s performance under slight interferences.Additionally,we highlight current research difficulties in the field of DFACS noise analysis.Overall,this paper provides valuable insights into the modeling and analysis of disturbances and noises in DFACSs,and identifies key areas for future research.
基金Supported by the National Key R&D Program of China:Gravitational Wave Detection Project(Nos.2021YFC22026,2021YFC2202601,and 2021YFC2202603)the National Natural Science Foundation of China(No.12172288).
文摘This study investigates the orbital Target-Attacker-Defender(TAD)game problem in the context of space missions.In this game,the Attacker and the Defender compete for a Target that is unable to maneuver due to its original mission constraints.This paper establishes three TAD game models based on the thrust output capabilities:unconstrained thrust output,thrust constrained by an upper bound,and fixed thrust magnitude.These models are then solved using differential game theory to obtain Nash equilibrium solutions for the game problems,and the correctness and effectiveness of the solution methods are verified through simulations.Furthermore,an analysis of the winning mechanisms of the game is conducted,identifying key factors that influence the game’s outcomes,including weight coefficients in payoffs,the maximum thrust acceleration limit,and the initial game state.Considering the unique characteristics of space missions,a specific focus is given to the analysis of the Defender’s initial states in the hovering formation and in-plane circling formation,revealing overall success patterns for defense strategies from these two formations.In summary,this study provides valuable insights into the control strategies and winning mechanisms of orbital TAD games,deepening our understanding of these games and offering practical guidance to improve success rates in real-world scenarios.
基金This research was supported by National Key R&D Program of China:Gravitational Wave Detection Project,China(Nos.2021YFC2202601,2021YFC2202603)National Natural Science Foundation of China(No.12172288).
文摘The Drag-Free and Attitude Control System(DFACS)is a critical platform for various space missions,including high precision satellite navigation,geoscience and gravity field measurement,and space scientific experiments.This paper presents a comprehensive review of over sixty years of research on the design and dynamics model of DFACS.Firstly,we examine the open literature on DFACS and its applications in Drag-Free missions,providing readers with necessary background information on the field.Secondly,we analyze the system configurations and main characteristics of different DFACSs,paying particular attention to the coupling mechanism between the system configuration and dynamics model.Thirdly,we summarize the dynamics modeling methods and main dynamics models of DFACS from multiple perspectives,including common fundamentals and specific applications.Lastly,we identify current challenges and technological difficulties in the system design and dynamics modeling of DFACS,while suggesting potential avenues for future research.This paper aims to provide readers with a comprehensive understanding of the state-of-the-art in DFACS research,as well as the future prospects and challenges in this field.
基金the National Natural Science Foundation of China(Grant No.12172288)the National Key Basic Research Program of China:Gravitational Wave Detection Project(Grant Nos.2021YFC2202600 and 2021YFC2202603).
文摘This study proposes a parametric formation control method for the cooperative observation of the China Space Station(CSS)using multiple nanosatellites.First,a simplified geometrical model of the CSS is constructed using fundamental solids,such as the capsule body and cuboid.Second,the spacecraft formation configuration for the observation mission is characterized by a three-dimensional(3D)Lissajous curve using related design parameters under the full-coverage observation requirements of specific parts,such as the CSS connecting section and collision avoidance constraints.Third,a double-layer control law is designed for each nanosatellite,in which the upper layer is a distributed observer for recognizing the target formation configuration parameters,and the lower layer is a trajectory-tracking controller to make the nanosatellite converge to its temporary target position calculated from the upper layer’s outputs.The closed-loop control stability is proven under the condition that the communication network topology of the nanosatellite cluster contains a directed spanning tree.Finally,the control method is verified by numerical simulation,where the CSS connecting section is selected as the observation target,and ten small nanosatellites are assumed to perform the cooperative observation mission.The simulation results demonstrate that the double-layer control law is robust to single-point communication failures and suitable for the accompanying missions of large space objects with multiple nanosatellites.
基金supported by the National Natural Science Foundation of China(No.12172288)the National Key Basic Research Program of China:Gravitational Wave Detection Project(No.2021YFC2202601 and No.2021YFC2202603).
文摘This paper discusses the modeling and solving of orbital pursuit-evasion games(OPEGs)under J_(2)perturbation.The optimal long-range maneuver method under J_(2)perturbation is designed,and it is proved that the effect of eccentricity can be ignored when transfer times and theΔV budgets are fixed.It is discovered that when the inclination between the initial and target orbit is equal and is between 10°and 25°,the whole maneuver process can be simplified to a fixed-inclination transfer.Subsequently,a long-term OPEG model is provided under the assumption of fixed inclination,zero eccentricity,and impulsive thrust.Winning conditions of OPEGs under J_(2)perturbation are then carefully derived,with long-time OPEG(J_(2)dominated)and short-time OPEG(traditional)separated,and typical tactics of both sides formulated and verified.These studies are further extended to the“Arrival time matching game”for maintaining/avoiding resonant arrival time under J_(2)perturbation,and the advantages and disadvantages of both sides are analyzed.The models and strategies obtained in this paper can be potentially used in practical applications of OPEGs,especially for evaders that have low thrust-weight ratios and are weak in traditional short-term OPEGs.
基金the National Natural Science Foundation of China(No.12172288)the National Key R&D Program of China(Nos.2021YFC2202601,2021YFC2202603).
文摘This paper proposes an efficient design method for nano satellites formation flying near a large space target to perform ultra-close inspection missions.A parametric model for periodic relative motion between two satellites is firstly proposed through a detailed analysis of the relative orbital dynamics.It is proved that the existing periodic solutions of satellite relative motion such as in-plane 2:1 elliptic and circular periodic relative orbits both belong to the ellipsoid family of periodic relative orbits.The motion planes and their locations and orientations of the general periodic relative orbits are then determined as the analytic functions of the initial relative states.The maximal and minimal distances from the relative orbit to the origin are further analytically calculated too.A formation design algorithm is then proposed for optimal observation of feature points of the target considering various requirements of collision avoidance and observable distance by using this parametric model.Numerical examples about target inspection are introduced to quantitively evaluate and verify the models and methods.The simulation results are well consistent with the theoretical predictions,showing that the design proposed can be potentially applied for future practical on-orbit service missions.
基金supported by the National Natural Science Foundation of China(no.12172288)the National Key Basic Research Program of China:Gravitational Wave Detection Project(nos.2021YFC2202601 and 2021YFC2202603).
文摘This paper explores the blocking capabilities of a spacecraft deployed near Earth-Moon L1 libration point against another spacecraft attempting lunar gravity assist,based on theΔV required for interception.The study demonstrates that a pursuer at L1 libration point can effectively block low-energy evaders with minimalΔV expenditure,creating a blockade against their use of gravity assists.However,blocking against high-energy evaders is relatively weaker.Pursuers on Lyapunov orbits can execute blockades that L1 pursuers cannot,albeit with lower mission-capable rates.The paper discusses mission-capable rates for different Lyapunov orbits and evader energies,revealing that each Lyapunov orbit has its unique optimal blocking energy,decreasing as the Lyapunov orbit size expands.In addition,the paper proposes a strategy for evaders to bypass blockades by sacrificing a portion of theirΔV and verifies it numerically.The analysis covers the cost and benefits of the L1 libration point-related blockade,the importance of the mission-capable rate,and the possibility of lunar-orbit blocking.These findings provide insights for future research on orbital games in the Earth-Moon system and orbital blockade.
基金This work was supported by the National Natural Science Foundation of China(Grant No.61403416)the“The Hundred Talents Program”of Chinese Academy of Science.
文摘A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.
