Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerica...Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.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
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
The heavy rainfall in Beijing on 21 July 2012 was a high impact event. First, a synoptic overview of this event is presented based on the ECMWF reanalysis and forecast data, together with observations of hourly precip...The heavy rainfall in Beijing on 21 July 2012 was a high impact event. First, a synoptic overview of this event is presented based on the ECMWF reanalysis and forecast data, together with observations of hourly precipitation. It is found that an east to northeastward moving ＂low-level northwest vortex＂ caused this event. The vortex was formed under favorable circulation patterns and intensified by low-level dry intrusions. The source regions of the large volume of moisture necessary to sustain the intense rainfall are diagnosed by back-trajectory analysis. Approximately 77% of the moisture was transported from the Bay of Bengal （BOB）. The transport processes, including vertical profiles, mean humidity variations, and relative importance of the rain-paths, are further quantified by the back-trajectory analysis and cluster analysis. The results highlight the importance of the southwestern path in transporting moisture to northern China, which accounts for 88.4% of the moisture from the BoB, and 68% of the total of the ＂7.21＂ heavy rainfall event.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos. 10832004 and 11072122)
文摘Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.
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.
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 Joint Scientific Thematic Research Programme(JSTP)International Cooperation Program of the Ministry of Science and Technology of China(2011DFG23440)State Scholarship Fund of China Scholarship Council(CSC)
文摘The heavy rainfall in Beijing on 21 July 2012 was a high impact event. First, a synoptic overview of this event is presented based on the ECMWF reanalysis and forecast data, together with observations of hourly precipitation. It is found that an east to northeastward moving ＂low-level northwest vortex＂ caused this event. The vortex was formed under favorable circulation patterns and intensified by low-level dry intrusions. The source regions of the large volume of moisture necessary to sustain the intense rainfall are diagnosed by back-trajectory analysis. Approximately 77% of the moisture was transported from the Bay of Bengal （BOB）. The transport processes, including vertical profiles, mean humidity variations, and relative importance of the rain-paths, are further quantified by the back-trajectory analysis and cluster analysis. The results highlight the importance of the southwestern path in transporting moisture to northern China, which accounts for 88.4% of the moisture from the BoB, and 68% of the total of the ＂7.21＂ heavy rainfall event.
