A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse...A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.展开更多
The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximi...The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximity operations. In thispaper, to obtain high-fidelity dynamics, higher-order relative motion model is developed via nonlinear mapping of orbitelement differences and Hill coordinates. First, second-order variation of parameter technique of calculus of variations isapplied to the direction cosine matrix (DCM), which maps vector components in inertial frame to vector components inDeputy Hill frame, and deputy spacecraft inertial position and velocity vectors in Deputy Hill frame. Second, after series oftransformations and elimination of higher-order terms greater than quadratic terms, new, nonlinearly mapped radial, alongtrackand cross-track relative motion position and velocity equations are obtained. Using the newequation ofmotion, nonlinearstate space model is developed. The new equations, validated via numerical simulations, are amenable for the analysis ofspacecraft relative motion, formation flying, rendezvous and proximity operations in both circular and elliptical orbits.展开更多
Low earth orbit satellites,with unique advantages,are prosperous types of navigation augmentation satellites for the GNSS satellites constellations.The broadcast ephemeris element needs to be designed as an important ...Low earth orbit satellites,with unique advantages,are prosperous types of navigation augmentation satellites for the GNSS satellites constellations.The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs.The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component.Besides,the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits.Based on the nonsingular orbital elements,5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components.The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18*/19-element ephemerides are better than 10/6/4/5/2.5 cm,respectively.According to the dynamical range of the fitting elements,the interfaces were designed for the 5 sets of ephemerides.The effects of data truncation on fitting UREs are at millimeter level.The total bits are 329/343/376/379/396,respectively.29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris,while 64/61/41 bits can be saved for the 18/18*/19-element ephemerides compared with the GPS18 elements ephemeris.展开更多
The tethered satellite system has a great potential and one of its very useful applications is momentum transfer. Raising a payload by deploying it upward from an orbitor on a long tether and then releasing it represe...The tethered satellite system has a great potential and one of its very useful applications is momentum transfer. Raising a payload by deploying it upward from an orbitor on a long tether and then releasing it represents a rather important possible application with significant fael economy. This paper presents a dynamic model set up for a two body tethered satellite system and two control laws of deployment used to simulate the deployment of the system, gives calculation formulas for six orbital elements of two sub satellites and discusses calculation examples.展开更多
An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in ...An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.展开更多
A middle-aged male patient with a right orbital comminuted fracture underwent computer tomography scanning, and a three-dimensional finite element model of the eyes and relevant tissues was established. Optic nerve st...A middle-aged male patient with a right orbital comminuted fracture underwent computer tomography scanning, and a three-dimensional finite element model of the eyes and relevant tissues was established. Optic nerve stress in a hyperbaric oxygen environment was simulated and analyzed by changing the elastic modulus and external pressure of the skull at the damage side. Results showed that stress maximized at the contact site of the optic nerve and the eyeball in the damaged and intact eye orbits. Optic nerve stress at the damaged orbit significantly increased; however, stress in the intact orbit only slightly changed with decreased elastic modulus of the skull while external pressure remained unchanged. Maximum optic nerve stress increased in the damaged and intact side, along with increased external pressure, while elastic modulus remained unchanged. These experimental findings suggested that the optic nerve was compressed under hyperbaric oxygen and optic nerve stress was greater in the damaged orbit than in the intact orbit.展开更多
An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, ...An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, the feedback control law based on Gauss’s perturbation equations of motion is given. And the impulse control for targeting from the higher circulation orbit to the specified periapsis is developed. Finally, the numerical simulation is performed and the simulation results show that the presented impulse control law is effective.展开更多
In this paper, the relative orbital configurations of satellites in formation flying with non-perturbation and J<SUB>2</SUB> perturbation are studied, and an orbital elements method is proposed to obtain t...In this paper, the relative orbital configurations of satellites in formation flying with non-perturbation and J<SUB>2</SUB> perturbation are studied, and an orbital elements method is proposed to obtain the relative orbital configurations of satellites in formation. Firstly, under the condition of non-perturbation, we obtain many shapes of relative orbital configurations when the semi-major axes of satellites are equal. These shapes can be lines, ellipses or distorted closed curves. Secondly, on the basis of the analysis of J<SUB>2</SUB> effect on relative orbital configurations, we find out that J<SUB>2</SUB> effect can induce two kinds of changes of relative orbital configurations. They are distortion and drifting, respectively. In addition, when J<SUB>2</SUB> perturbation is concerned, we also find that the semi-major axes of the leading and following satellites should not be the same exactly in order to decrease the J<SUB>2</SUB> effect. The relationship of relative orbital elements and J<SUB>2</SUB> effect is obtained through simulations. Finally, the minimum relation perturbation conditions are established in order to reduce the influence of the J<SUB>2</SUB> effect. The results show that the minimum relation perturbation conditions can reduce the J<SUB>2</SUB> effect significantly when the orbital element differences are small enough, and they can become rules for the design of satellite formation flying.展开更多
Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed ...Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.展开更多
To investigate the real-time mean orbital elements(MOEs)estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit trans-fer,a modified augmented square-root u...To investigate the real-time mean orbital elements(MOEs)estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit trans-fer,a modified augmented square-root unscented Kalman filter(MASUKF)is proposed.The MASUKF is composed of sigma points calculation,time update,modified state jumping detec-tion,and measurement update.Compared with the filters used in the existing literature on MOEs estimation,it has three main characteristics.Firstly,the state vector is augmented from six to nine by the added thrust acceleration terms,which makes the fil-ter additionally give the state-jumping-thrust-acceleration esti-mation.Secondly,the normalized innovation is used for state jumping detection to set detection threshold concisely and make the filter detect various state jumping with low latency.Thirdly,when sate jumping is detected,the covariance matrix inflation will be done,and then an extra time update process will be con-ducted at this time instance before measurement update.In this way,the relatively large estimation error at the detection moment can significantly decrease.Finally,typical simulations are per-formed to illustrated the effectiveness of the method.展开更多
The two line elements(TLEs),released by the North American Aerospace Defense Command(NORAD),are chosen for CubeSats' mission operators.Unfortunately,they have errors and other accompanied problems,which cause larg...The two line elements(TLEs),released by the North American Aerospace Defense Command(NORAD),are chosen for CubeSats' mission operators.Unfortunately,they have errors and other accompanied problems,which cause large deviations in the in-track component.When a TLE value is available at a certain epoch,the dominant error is the angular error.It is proposed to correct the angular error by solving-for the mean argument of latitude at the desired epoch.A batch least squares technique and range rate measurements are used for the correction process.With the assistance of satellite tool kit(STK)software and Matlab,a simulation to verify the orbit determination(OD)technique is implemented.This paper provides an angular correction low cost OD method and presents a complete analysis for various test cases.This approach maintains high accuracy in cross-track and radial and makes great improvement in in-track at the same time,but it is exclusive for circular orbits.When it is applied to an elliptical orbit,the error will be unacceptable.Therefore,the angular error is corrected using the longitude of periapsis which totally mitigates the error at the epoch under consideration.For inclinations less than 20 o,the mean longitude is preferred for the angular correction as it provides more accuracy compared with the mean argument of latitude.展开更多
Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illust...Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.展开更多
The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years.This paper presents the development and analysis of a model predictive control based framework that...The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years.This paper presents the development and analysis of a model predictive control based framework that is used with the D’Amico relative orbital elements(ROEs)to maintain the desired trajectories of a cluster of spacecraft while also allowing freedom to maneuver within some allowable bounds.Switching surfaces based on the ROE constraints contain the full state of the system,allowing for fuel reduction over other approaches that use the Hill—Clohessy—Wiltshire equations.The formation and boundary constraints are designed such that no two agents have overlapping regions,allowing the vehicles to maintain safety of flight without continually maintaining the trajectories of other agents.This framework allows for a scalable method that can support clusters of satellites to safely achieve mission objectives while minimizing fuel usage.This paper provides simulated results of the framework for a three spacecraft formation that demonstrates a 67%fuel reduction when compared to previous approaches.展开更多
基金supported by the Innovation Foundation of BUAA for PhD Graduates (No.YWF-12-RBYJ-024)the National Natural Science Foundation of China (No.11002008)National Basic Research Program of China (No.2009CB723906)
文摘A new set of relative orbit elements（ROEs）is used to derive a new elliptical formation flying model.In-plane and out-of-plane motions can be completely decoupled,which benefts elliptical formation design.The inverse transformation of the state transition matrix is derived to study the relative orbit control strategy.Impulsive feedback control laws are developed for both in-plane and out-of-plane relative motions.Control of in-plane and out-of-plane relative motions can be completely decoupled using the ROE-based feedback control law.A tangential impulsive control method is proposed to study the relationship of fuel consumption and maneuvering positions.An optimal analytical along-track impulsive control strategy is then derived.Different typical orbit maneuvers,including formation establishment,reconfguration,long-distance maneuvers,and formation keeping,are taken as examples to demonstrate the performance of the proposed control laws.The effects of relative measurement errors are also considered to validate the high accuracy of the proposed control method.
文摘The ultimate need to design and develop high-fidelity dynamical models for future space missions is necessitated by thecontinuous and enormous interest in spacecraft formation flying, rendezvous and spacecraft proximity operations. In thispaper, to obtain high-fidelity dynamics, higher-order relative motion model is developed via nonlinear mapping of orbitelement differences and Hill coordinates. First, second-order variation of parameter technique of calculus of variations isapplied to the direction cosine matrix (DCM), which maps vector components in inertial frame to vector components inDeputy Hill frame, and deputy spacecraft inertial position and velocity vectors in Deputy Hill frame. Second, after series oftransformations and elimination of higher-order terms greater than quadratic terms, new, nonlinearly mapped radial, alongtrackand cross-track relative motion position and velocity equations are obtained. Using the newequation ofmotion, nonlinearstate space model is developed. The new equations, validated via numerical simulations, are amenable for the analysis ofspacecraft relative motion, formation flying, rendezvous and proximity operations in both circular and elliptical orbits.
文摘Low earth orbit satellites,with unique advantages,are prosperous types of navigation augmentation satellites for the GNSS satellites constellations.The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs.The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component.Besides,the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits.Based on the nonsingular orbital elements,5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components.The fitting experiments based on the LEO of 300 to 1500 km altitudes show that the fitting UREs of the proposed 16/17/18/18*/19-element ephemerides are better than 10/6/4/5/2.5 cm,respectively.According to the dynamical range of the fitting elements,the interfaces were designed for the 5 sets of ephemerides.The effects of data truncation on fitting UREs are at millimeter level.The total bits are 329/343/376/379/396,respectively.29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris,while 64/61/41 bits can be saved for the 18/18*/19-element ephemerides compared with the GPS18 elements ephemeris.
文摘The tethered satellite system has a great potential and one of its very useful applications is momentum transfer. Raising a payload by deploying it upward from an orbitor on a long tether and then releasing it represents a rather important possible application with significant fael economy. This paper presents a dynamic model set up for a two body tethered satellite system and two control laws of deployment used to simulate the deployment of the system, gives calculation formulas for six orbital elements of two sub satellites and discusses calculation examples.
文摘An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.
基金the National Natural Science Foundation of China (Key Program),No.11032008the National Natural Science Foundation of China (General Program),No. 10872140+1 种基金10702048the Natural Science Foundation of Shanxi Province,No.2010021004-1
文摘A middle-aged male patient with a right orbital comminuted fracture underwent computer tomography scanning, and a three-dimensional finite element model of the eyes and relevant tissues was established. Optic nerve stress in a hyperbaric oxygen environment was simulated and analyzed by changing the elastic modulus and external pressure of the skull at the damage side. Results showed that stress maximized at the contact site of the optic nerve and the eyeball in the damaged and intact eye orbits. Optic nerve stress at the damaged orbit significantly increased; however, stress in the intact orbit only slightly changed with decreased elastic modulus of the skull while external pressure remained unchanged. Maximum optic nerve stress increased in the damaged and intact side, along with increased external pressure, while elastic modulus remained unchanged. These experimental findings suggested that the optic nerve was compressed under hyperbaric oxygen and optic nerve stress was greater in the damaged orbit than in the intact orbit.
文摘An impulse feedback control law to change the mean orbit elements of spacecraft around asteroid is presented. First, the mean orbit elements are transferred to the osculating orbit elements at the burning time. Then, the feedback control law based on Gauss’s perturbation equations of motion is given. And the impulse control for targeting from the higher circulation orbit to the specified periapsis is developed. Finally, the numerical simulation is performed and the simulation results show that the presented impulse control law is effective.
基金The project supported by the National Natural Science Foundation of China(10202008)Specialized Research Fund for the Doctoral Program of Higher Education(20020003024)
文摘In this paper, the relative orbital configurations of satellites in formation flying with non-perturbation and J<SUB>2</SUB> perturbation are studied, and an orbital elements method is proposed to obtain the relative orbital configurations of satellites in formation. Firstly, under the condition of non-perturbation, we obtain many shapes of relative orbital configurations when the semi-major axes of satellites are equal. These shapes can be lines, ellipses or distorted closed curves. Secondly, on the basis of the analysis of J<SUB>2</SUB> effect on relative orbital configurations, we find out that J<SUB>2</SUB> effect can induce two kinds of changes of relative orbital configurations. They are distortion and drifting, respectively. In addition, when J<SUB>2</SUB> perturbation is concerned, we also find that the semi-major axes of the leading and following satellites should not be the same exactly in order to decrease the J<SUB>2</SUB> effect. The relationship of relative orbital elements and J<SUB>2</SUB> effect is obtained through simulations. Finally, the minimum relation perturbation conditions are established in order to reduce the influence of the J<SUB>2</SUB> effect. The results show that the minimum relation perturbation conditions can reduce the J<SUB>2</SUB> effect significantly when the orbital element differences are small enough, and they can become rules for the design of satellite formation flying.
文摘Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.
基金This work was supported by National Natural Science Foundation of China(12372045)Shanghai Aerospace Science and Technology Program(SAST2021-030).
文摘To investigate the real-time mean orbital elements(MOEs)estimation problem under the influence of state jumping caused by non-fatal spacecraft collision or protective orbit trans-fer,a modified augmented square-root unscented Kalman filter(MASUKF)is proposed.The MASUKF is composed of sigma points calculation,time update,modified state jumping detec-tion,and measurement update.Compared with the filters used in the existing literature on MOEs estimation,it has three main characteristics.Firstly,the state vector is augmented from six to nine by the added thrust acceleration terms,which makes the fil-ter additionally give the state-jumping-thrust-acceleration esti-mation.Secondly,the normalized innovation is used for state jumping detection to set detection threshold concisely and make the filter detect various state jumping with low latency.Thirdly,when sate jumping is detected,the covariance matrix inflation will be done,and then an extra time update process will be con-ducted at this time instance before measurement update.In this way,the relatively large estimation error at the detection moment can significantly decrease.Finally,typical simulations are per-formed to illustrated the effectiveness of the method.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China (No.20113219110025)
文摘The two line elements(TLEs),released by the North American Aerospace Defense Command(NORAD),are chosen for CubeSats' mission operators.Unfortunately,they have errors and other accompanied problems,which cause large deviations in the in-track component.When a TLE value is available at a certain epoch,the dominant error is the angular error.It is proposed to correct the angular error by solving-for the mean argument of latitude at the desired epoch.A batch least squares technique and range rate measurements are used for the correction process.With the assistance of satellite tool kit(STK)software and Matlab,a simulation to verify the orbit determination(OD)technique is implemented.This paper provides an angular correction low cost OD method and presents a complete analysis for various test cases.This approach maintains high accuracy in cross-track and radial and makes great improvement in in-track at the same time,but it is exclusive for circular orbits.When it is applied to an elliptical orbit,the error will be unacceptable.Therefore,the angular error is corrected using the longitude of periapsis which totally mitigates the error at the epoch under consideration.For inclinations less than 20 o,the mean longitude is preferred for the angular correction as it provides more accuracy compared with the mean argument of latitude.
基金supported by the National Natural Science Foundation of China (10702078)the Research Foundation of National University of Defense Technology (JC08-01-05)
文摘Sun synchronous orbit and frozen orbit formed due to J 2 perturbation have very strict constraints on orbital parameters,which have restricted the application a lot.In this paper,several control strategies were illustrated to realize Sun synchronous frozen orbit with arbitrary orbital elements using continuous low-thrust.Firstly,according to mean element method,the averaged rate of change of the orbital elements,originating from disturbing constant accelerations over one orbital period,was derived from Gauss＇ variation of parameters equations.Then,we proposed that binormal acceleration could be used to realize Sun synchronous orbit,and radial or transverse acceleration could be adopted to eliminate the rotation of the argument of the perigee.Finally,amending methods on the control strategies mentioned above were presented to eliminate the residual secular growth.Simulation results showed that the control strategies illustrated in this paper could realize Sun synchronous frozen orbit with arbitrary orbital elements,and can save much more energy than the schemes presented in previous studies,and have no side effect on other orbital parameters＇ secular motion.
文摘The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years.This paper presents the development and analysis of a model predictive control based framework that is used with the D’Amico relative orbital elements(ROEs)to maintain the desired trajectories of a cluster of spacecraft while also allowing freedom to maneuver within some allowable bounds.Switching surfaces based on the ROE constraints contain the full state of the system,allowing for fuel reduction over other approaches that use the Hill—Clohessy—Wiltshire equations.The formation and boundary constraints are designed such that no two agents have overlapping regions,allowing the vehicles to maintain safety of flight without continually maintaining the trajectories of other agents.This framework allows for a scalable method that can support clusters of satellites to safely achieve mission objectives while minimizing fuel usage.This paper provides simulated results of the framework for a three spacecraft formation that demonstrates a 67%fuel reduction when compared to previous approaches.
