High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbita...High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.展开更多
The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And...The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.展开更多
In this study,the authors focus on the cut-off low pressure systems（COLs）lingering over East Asia in late spring and early summer and quantify the two-way stratosphere–troposphere exchange（STE）by 3D trajectory in...In this study,the authors focus on the cut-off low pressure systems（COLs）lingering over East Asia in late spring and early summer and quantify the two-way stratosphere–troposphere exchange（STE）by 3D trajectory integrations,achieved using a revised version of the UK Universities Global Atmospheric Modelling Programme Offline Trajectory Code（Version 3）.By selecting 10 typical COLs and calculating the cross-tropopause air mass fluxes,it is found that stratosphere-to-troposphere transport（STT）fluxes exist in the center of COLs;and in the periphery of the COL center,troposphereto-stratosphere transport（TST）fluxes and STT fluxes are distributed alternately.Net transport fluxes in COLs are from stratosphere to troposphere,and the magnitude is about 10-4 kg m-2 s-1.The ratio between the area-averaged STT and TST fluxes increases with increasing strength of the COLs.By adopting appropriate residence time,the spurious transports are effectively excluded.Finally,the authors compare the results with previous studies,and find that the cross-tropopause fluxes（CTFs）induced by COLs are about one to two orders of magnitude larger than global CTFs.COLs play a significant role in local,rapid air mass exchanges,although they may only be responsible for a fraction of the total STE.展开更多
This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth’s oblateness perturbation and shadow are taken into acco...This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth’s oblateness perturbation and shadow are taken into account.It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance optimality,robustness,and onboard computational efficiency.In this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation.Based on this relationship,the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory.Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators.In the transfer,the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time.Moreover,all these computations onboard are analytical.The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.展开更多
To expand mission capabilities needed without a proportional increase in cost or risk for exploration of the solar system,the multiple objective trajectory using low-thrust propulsion and gravity-assist technique is c...To expand mission capabilities needed without a proportional increase in cost or risk for exploration of the solar system,the multiple objective trajectory using low-thrust propulsion and gravity-assist technique is considered.However,low-thrust,gravity-assist trajectories pose significant optimization challenges because of their large design space.Here,the planets are selected as primal scientific mission goals,while the asteroids are selected as secondary scientific mission goals,and a global trajectory optimization problem is introduced and formulated.This multi-objective decision making process is transformed into a bi-level programming problem,where the targets like planets with small subsamples but high weight are optimized in up level,and targets like asteroids with large subsamples but low weight are optimized in down level.Then,the selected solutions for bi-level programming are optimized thanks to a cooperative Differential Evolution(DE) algorithm that is developed from the original DE algorithm;in addition,an sequential quadratic programming(SQP) method is used in low-thrust optimization.This solution approach is successfully applied to the simulation case of the multi-objective trajectory design problem.The results obtained are presented and discussed.展开更多
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered as a challenging problem.This paper describes a high-precision symplectic method and optimization techniques to s...Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered as a challenging problem.This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.展开更多
基金supported by the National Key Research and Development Project(Grant No.2018YFB1900605)the Key Research Program of Chinese Academy of Sciences(Grant No.ZDRW-KT-2019-1).
文摘High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.
文摘The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.
基金supported by the Special Fund for Strategic Pilot Technology,Chinese Academy of Sciences[grant number XDA05040300]
文摘In this study,the authors focus on the cut-off low pressure systems（COLs）lingering over East Asia in late spring and early summer and quantify the two-way stratosphere–troposphere exchange（STE）by 3D trajectory integrations,achieved using a revised version of the UK Universities Global Atmospheric Modelling Programme Offline Trajectory Code（Version 3）.By selecting 10 typical COLs and calculating the cross-tropopause air mass fluxes,it is found that stratosphere-to-troposphere transport（STT）fluxes exist in the center of COLs;and in the periphery of the COL center,troposphereto-stratosphere transport（TST）fluxes and STT fluxes are distributed alternately.Net transport fluxes in COLs are from stratosphere to troposphere,and the magnitude is about 10-4 kg m-2 s-1.The ratio between the area-averaged STT and TST fluxes increases with increasing strength of the COLs.By adopting appropriate residence time,the spurious transports are effectively excluded.Finally,the authors compare the results with previous studies,and find that the cross-tropopause fluxes（CTFs）induced by COLs are about one to two orders of magnitude larger than global CTFs.COLs play a significant role in local,rapid air mass exchanges,although they may only be responsible for a fraction of the total STE.
基金supported by the National Natural Science Foundation of China(No.12022214)the National Key R&D Program of China(No.2020YFC2201200)。
文摘This paper proposes an optimal,robust,and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit.The Earth’s oblateness perturbation and shadow are taken into account.It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time,including high guidance optimality,robustness,and onboard computational efficiency.In this work,a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified,which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation.Based on this relationship,the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory.Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators.In the transfer,the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time.Moreover,all these computations onboard are analytical.The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality,robustness,and onboard computational efficiency.
基金supported by the Open Research Foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China (Grant No. 2012afdl005)
文摘To expand mission capabilities needed without a proportional increase in cost or risk for exploration of the solar system,the multiple objective trajectory using low-thrust propulsion and gravity-assist technique is considered.However,low-thrust,gravity-assist trajectories pose significant optimization challenges because of their large design space.Here,the planets are selected as primal scientific mission goals,while the asteroids are selected as secondary scientific mission goals,and a global trajectory optimization problem is introduced and formulated.This multi-objective decision making process is transformed into a bi-level programming problem,where the targets like planets with small subsamples but high weight are optimized in up level,and targets like asteroids with large subsamples but low weight are optimized in down level.Then,the selected solutions for bi-level programming are optimized thanks to a cooperative Differential Evolution(DE) algorithm that is developed from the original DE algorithm;in addition,an sequential quadratic programming(SQP) method is used in low-thrust optimization.This solution approach is successfully applied to the simulation case of the multi-objective trajectory design problem.The results obtained are presented and discussed.
基金supported by the National Natural Science Foundation of China(Grant Nos.11672146,11432001)the 2015 Chinese National Postdoctoral International Exchange Program
文摘Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered as a challenging problem.This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.
