Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection ...Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna （LISA）. The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry （TDI） to match the two different optical paths （times of travel）. Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 （here, CGC stands for center for gravitation and cosmology） ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.展开更多
ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massiv...ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.展开更多
The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation...The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation in China,this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm.In this paper,four different optimal LEO constellation configurations are designed,and their enhancements to BDS3 navigation performance are analyzed,including Geometric Dilution of Precision(GDOP),the numbers of visible satellites,and the rapid convergence of precision point positioning(PPP).Additionally,the enhancement advantages in China compared to other regions are further discussed.The results demonstrate that regional enhanced constellations with 70,72,80,and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation.Globally,the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0%,18.3%,19.9%,and 20.3%.Similar results can be obtained using the genetic algorithm(GA),but the computational efficiency of Bayesian optimization algorithm is 53.9%higher than that of the genetic algorithm.The number of visible satellites of enhanced constellations in China has increased by more than four on average,which is better than that in other regions.In the PPP experiment,the convergence time of the stations in China and other regions is shortened by 83.0%and 76.2%,respectively,and the navigation performance of hybrid constellations in China is better.展开更多
Low Earth Orbit(LEO)satellite for navigation augmentation applications can significantly reduce the precise positioning convergence time and attract increasing attention recently.A few LEO Navigation Augmentation(LEO-...Low Earth Orbit(LEO)satellite for navigation augmentation applications can significantly reduce the precise positioning convergence time and attract increasing attention recently.A few LEO Navigation Augmentation(LEO-NA)constellations have been proposed,while corresponding constellation design methodologies have not been systematically studied.The LEO-NA constellation generally consists of a huge number of LEO satellites and it strives for multiple optimization purposes.It is essentially different from the communication constellation or earth observing constellation design problem.In this study,we modeled the LEO-NA constellation design problem as a multi-objective optimization problem and solve this problem with the MultiObjective Particle Swarm Optimization(MOPSO)algorithm.Three objectives are used to strive for the best tradeoff between the augmentation performance and deployment efficiency,namely the Position Dilution of Precision(PDOP),visible LEO satellites and the orbit altitude.A fuzzy set approach is used to select the final constellation from a set of Pareto optimal solutions given by the MOPSO algorithm.To evaluate the performance of the optimized constellation,we tested two constellations with 144 and 288 satellites and each constellation has three optimization schemes:the polar constellation,the single-layer constellation and the two-layer constellation.The results indicate that the optimized two-layer constellation achieves the best global coverage and is followed by the single-layer constellation.The MOPSO algorithm can help to improve the constellation design and is suitable for solving the LEO-NA constellation design problem.展开更多
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
This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized p...This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized patched manifolds in CR3BP(circular restricted three-body problems), the shape-based method with multi-body environment, the homotopic method with multi-body environment, and the low-thrust capturing and descending algorithm with multi-body environment are all included. Firstly, the parameters describing the patched manifolds in CR3 BP are optimized until the least total absolute velocity increment has been got, including the employment of the shape-based method with multi-body environment. Secondly, the low-thrust control laws of the transfer orbit are optimized employing the homotopic method with multi-body environment that transfers the fuel optimization problem to an easier energy optimization problem. Thirdly, the low-thrust descending orbit around Mars is computed using the laws proposed in this paper. As a typical example, the Earth-Mars transfer orbit design is discussed. The results showed that the parameters describing the patched manifolds could be optimized by the DE(differential evolution) algorithm effectively; the homotopic method with multi-body environment could get the optimal value that meets the first order optimality conditions; and the low-thrust descending orbit could effectively be captured by Mars and finally become a circular parking orbit around it by the hypothesis control laws proposed in this paper. It shows that the final fuel cost is much less than the optimal transfer in the patched two-body problems. In conclusion, the method proposed in this paper could effectively solve the low-energy low-thrust optimal control problem in multi-body environment for the future deep space explorations.展开更多
In this study,a combined trajectory and time-planning strategy is proposed to reduce the fuel consumption of low-thrust rendezvous missions.First,a transformation method was developed to adjust the independent variabl...In this study,a combined trajectory and time-planning strategy is proposed to reduce the fuel consumption of low-thrust rendezvous missions.First,a transformation method was developed to adjust the independent variable such that results obtained using the shape-based algorithm that employs an inverse polynomial can be used as an initial guess for a pseudospectral method.Second,a planning strategy that combined low-thrust transfer trajectory optimization and boundary condition optimization was designed.This planning strategy was divided into outer and inner layers.The outer plan optimized waiting and transfer times and thus determined boundary conditions.The inner plan optimized the low-thrust transfer trajectory using the pseudospectral method.The inner plan was embedded in the outer plan.Numerical simulations show that the independent variable transformation method is feasible,and the combined use of the shape-based algorithm with the inverse polynomial and pseudospectral method ensures good convergence.The cost of rendezvous missions is significantly decreased using combined trajectory and time optimization.展开更多
In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients i...In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients is developed to re ect the gravitational e ect more precisely.The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in xed-time.By introducing the initial and nal coasts,the optimal interplanetary transfer is extended to the time-free situation.Finally,the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer.Comparisons with existing methods show that the proposed method can provide better transfer performances with high eciency.The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.展开更多
The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission.A model for computing the two-impulse trans-lunar orbit,which strictly s...The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission.A model for computing the two-impulse trans-lunar orbit,which strictly satisfies the boundary constraints,is established.The solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial continuation.By taking the solution set of a circular restricted three-body model as the initial values of the design variables,the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology.A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer window.Moreover,there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost.A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.展开更多
Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods p...Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.展开更多
The Solar Ring mission, a concept to monitor the Sun and inner heliosphere from multiple perspectives, has been funded for prephase study by the Strategic Priority Program of Chinese Academy of Sciences in space scien...The Solar Ring mission, a concept to monitor the Sun and inner heliosphere from multiple perspectives, has been funded for prephase study by the Strategic Priority Program of Chinese Academy of Sciences in space sciences. The Solar Ring is comprised of 6 spacecraft, grouped in three pairs, moving around the Sun in an elliptical orbit in the ecliptic plane. The mission costs,including launch fee, deep-space maneuvers, and deployment time of the ring, are highly relevant to the working orbit, deepspace transfer, and phase angle within a group. The preliminary mission profile is analyzed and designed in this paper. The launch way, two spacecraft with one rocket, is adopted. The deployment time, phasing maneuvers, and C_(3) of launch energy are evaluated for the elliptical orbits with the perihelion between 0.7 and 0.9 AU using the rockets of Long March(LM) 3A and 3B.Numerical simulations show two candidate trajectories: fast deployment within 4 years by LM-3B, medium deployment more than 6 years by cheaper rocket of LM-3A. In order to obtain both fast deployment and low launch cost, another orbit profile is proposed by shortening the phase angle within a group. The suggested working orbits and the corresponding costs of launch,deployment time, and phasing maneuvers will strongly support the science objectives.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10778710 and 10875171)
文摘Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection （ASTROD- GW） is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna （LISA）. The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry （TDI） to match the two different optical paths （times of travel）. Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 （here, CGC stands for center for gravitation and cosmology） ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.
文摘ASTROD-GW （ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection） is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirais （EMRIs） and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4, and L5. The 3 space, crafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD- GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry （TDI） for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precessionperiod. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° （no inclination）, 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.
基金founded by the National Natural Science Foundation of China(42030109)the Startup Foundation for Doctors of Liaoning Province(2021-BS-275)+4 种基金the Scientific Study Project for Institutes of Higher LearningMinistry of EducationLiaoning Province(LJKMZ20220673)the Project supported by the State Key Laboratory of Geodesy and Earths'DynamicsInnovation Academy for Precision Measurement Science and Technology(SKLGED2023-3-2)。
文摘The application of Low Earth Orbit(LEO)satellite navigation can enhance geometric structure,increase observations and contribute to navigation and positioning.To improve the performance of the navigation constellation in China,this study proposes an optimized method of LEO-enhanced navigation constellation for BDS based on Bayesian optimization algorithm.In this paper,four different optimal LEO constellation configurations are designed,and their enhancements to BDS3 navigation performance are analyzed,including Geometric Dilution of Precision(GDOP),the numbers of visible satellites,and the rapid convergence of precision point positioning(PPP).Additionally,the enhancement advantages in China compared to other regions are further discussed.The results demonstrate that regional enhanced constellations with 70,72,80,and 81 satellites at an altitude of 1000 km can significantly improve the navigation performance of the navigation constellation.Globally,the addition of optimized LEO constellations has reduced the hybrid constellation GDOP by 19.0%,18.3%,19.9%,and 20.3%.Similar results can be obtained using the genetic algorithm(GA),but the computational efficiency of Bayesian optimization algorithm is 53.9%higher than that of the genetic algorithm.The number of visible satellites of enhanced constellations in China has increased by more than four on average,which is better than that in other regions.In the PPP experiment,the convergence time of the stations in China and other regions is shortened by 83.0%and 76.2%,respectively,and the navigation performance of hybrid constellations in China is better.
基金the National Natural Science Foundation of China(Nos.41704002,91638203,41904038)。
文摘Low Earth Orbit(LEO)satellite for navigation augmentation applications can significantly reduce the precise positioning convergence time and attract increasing attention recently.A few LEO Navigation Augmentation(LEO-NA)constellations have been proposed,while corresponding constellation design methodologies have not been systematically studied.The LEO-NA constellation generally consists of a huge number of LEO satellites and it strives for multiple optimization purposes.It is essentially different from the communication constellation or earth observing constellation design problem.In this study,we modeled the LEO-NA constellation design problem as a multi-objective optimization problem and solve this problem with the MultiObjective Particle Swarm Optimization(MOPSO)algorithm.Three objectives are used to strive for the best tradeoff between the augmentation performance and deployment efficiency,namely the Position Dilution of Precision(PDOP),visible LEO satellites and the orbit altitude.A fuzzy set approach is used to select the final constellation from a set of Pareto optimal solutions given by the MOPSO algorithm.To evaluate the performance of the optimized constellation,we tested two constellations with 144 and 288 satellites and each constellation has three optimization schemes:the polar constellation,the single-layer constellation and the two-layer constellation.The results indicate that the optimized two-layer constellation achieves the best global coverage and is followed by the single-layer constellation.The MOPSO algorithm can help to improve the constellation design and is suitable for solving the LEO-NA constellation design problem.
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.
基金supported by the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2010AA7040014)
文摘This paper discusses the problem of design and optimization of low-energy transfer orbit with multi-body environment. A new integrative method is proposed to effectively solve the problem, in which the parameterized patched manifolds in CR3BP(circular restricted three-body problems), the shape-based method with multi-body environment, the homotopic method with multi-body environment, and the low-thrust capturing and descending algorithm with multi-body environment are all included. Firstly, the parameters describing the patched manifolds in CR3 BP are optimized until the least total absolute velocity increment has been got, including the employment of the shape-based method with multi-body environment. Secondly, the low-thrust control laws of the transfer orbit are optimized employing the homotopic method with multi-body environment that transfers the fuel optimization problem to an easier energy optimization problem. Thirdly, the low-thrust descending orbit around Mars is computed using the laws proposed in this paper. As a typical example, the Earth-Mars transfer orbit design is discussed. The results showed that the parameters describing the patched manifolds could be optimized by the DE(differential evolution) algorithm effectively; the homotopic method with multi-body environment could get the optimal value that meets the first order optimality conditions; and the low-thrust descending orbit could effectively be captured by Mars and finally become a circular parking orbit around it by the hypothesis control laws proposed in this paper. It shows that the final fuel cost is much less than the optimal transfer in the patched two-body problems. In conclusion, the method proposed in this paper could effectively solve the low-energy low-thrust optimal control problem in multi-body environment for the future deep space explorations.
基金Science and Technology on Space Intelligent Control Laboratory Grants(HTKJ2021KL502010)the Research Project of Space Debris and Near-Earth Asteroid Defense(KJSP2020010303).
文摘In this study,a combined trajectory and time-planning strategy is proposed to reduce the fuel consumption of low-thrust rendezvous missions.First,a transformation method was developed to adjust the independent variable such that results obtained using the shape-based algorithm that employs an inverse polynomial can be used as an initial guess for a pseudospectral method.Second,a planning strategy that combined low-thrust transfer trajectory optimization and boundary condition optimization was designed.This planning strategy was divided into outer and inner layers.The outer plan optimized waiting and transfer times and thus determined boundary conditions.The inner plan optimized the low-thrust transfer trajectory using the pseudospectral method.The inner plan was embedded in the outer plan.Numerical simulations show that the independent variable transformation method is feasible,and the combined use of the shape-based algorithm with the inverse polynomial and pseudospectral method ensures good convergence.The cost of rendezvous missions is significantly decreased using combined trajectory and time optimization.
基金This work was supported by Chang Jiang Scholars Program,the National Natural Science Foundation of China(Grant No.11572038 and No.11772050)Graduate Technological Innovation Project of Beijing Institute of Technology.
文摘In this paper,the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame.Based on primer vector theory,a modi ed cost function with variable coecients is developed to re ect the gravitational e ect more precisely.The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in xed-time.By introducing the initial and nal coasts,the optimal interplanetary transfer is extended to the time-free situation.Finally,the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer.Comparisons with existing methods show that the proposed method can provide better transfer performances with high eciency.The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.
基金This work was supported by the National Natural Science Foundation of China(No.11902362)the National Science and Technology Innovation Special Zone Project.
文摘The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission.A model for computing the two-impulse trans-lunar orbit,which strictly satisfies the boundary constraints,is established.The solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial continuation.By taking the solution set of a circular restricted three-body model as the initial values of the design variables,the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology.A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer window.Moreover,there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost.A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.
基金supported by the Strategic Priority Program of Chinese Academy of Sciences (CAS)(Grant Nos. XDA15017300 and XDB41000000)the Youth Innovation Promotion Association CAS(Grant No. 2020295)。
文摘The Solar Ring mission, a concept to monitor the Sun and inner heliosphere from multiple perspectives, has been funded for prephase study by the Strategic Priority Program of Chinese Academy of Sciences in space sciences. The Solar Ring is comprised of 6 spacecraft, grouped in three pairs, moving around the Sun in an elliptical orbit in the ecliptic plane. The mission costs,including launch fee, deep-space maneuvers, and deployment time of the ring, are highly relevant to the working orbit, deepspace transfer, and phase angle within a group. The preliminary mission profile is analyzed and designed in this paper. The launch way, two spacecraft with one rocket, is adopted. The deployment time, phasing maneuvers, and C_(3) of launch energy are evaluated for the elliptical orbits with the perihelion between 0.7 and 0.9 AU using the rockets of Long March(LM) 3A and 3B.Numerical simulations show two candidate trajectories: fast deployment within 4 years by LM-3B, medium deployment more than 6 years by cheaper rocket of LM-3A. In order to obtain both fast deployment and low launch cost, another orbit profile is proposed by shortening the phase angle within a group. The suggested working orbits and the corresponding costs of launch,deployment time, and phasing maneuvers will strongly support the science objectives.
