In this study,a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing problem.Considering the remote communication restrictions and...In this study,a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing problem.Considering the remote communication restrictions and environmental uncertainties,advanced landing control techniques are demanded to meet the high requirements of real-time performance and autonomy in the Moon landing missions.Deep reinforcement learning(DRL)algorithms have been recently developed for real-time optimal control but suffer the obstacles of slow convergence and difficult reward function design.To address these problems,a DRL algorithm is developed using an actor-indirect method architecture to achieve the optimal control of the Moon landing mission.In this DRL algorithm,an indirect method is employed to generate the optimal control actions for the deep neural network(DNN)learning,while the trained DNNs provide good initial guesses for the indirect method to promote the efficiency of training data generation.Through sufficient learning of the state-action relationship,the trained DNNs can approximate the optimal actions and steer the spacecraft to the target in real time.Additionally,a nonlinear feedback controller is developed to improve the terminal landing accuracy.Numerical simulations are given to verify the effectiveness of the proposed DRL algorithm and demonstrate the performance of the developed optimal landing controller.展开更多
Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-boa...Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-board applications.In this study,the indirect method is improved to achieve real-time trajectory optimization of fuel-optimal powered planetary landings with the help of analytical shooting equation derivations and a practical homotopy technique.Specifically,the contributions of this paper are threefold.First,the analytical expressions for shooting equation calculation are derived to replace the traditional time-consuming trajectory integration.Consequently,the computational efficiency is significantly improved.Second,the original three-dimensional landing problem is connected with a simplified one-dimensional problem that only involves the vertical dynamics,and its analytical solution is obtained based on Pontryagin’s minimum principle.Third,starting with the analytical solution,the accurate solution of the original landing problem can be obtained through an adaptive homotopy process.Simulation results of Earth landing scenarios are given to substantiate the effectiveness of the proposed techniques and illustrate that the developed method can obtain a fuel-optimal landing trajectory in 5 ms with 100%success rate.展开更多
This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug.The scheme contains three stages named respectively as dragging,maintenance and swinging.In the first stage,the tug,p...This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug.The scheme contains three stages named respectively as dragging,maintenance and swinging.In the first stage,the tug,propelled by continuous thrust,tows deorbit to a transfer orbit with a tether.Then in the second stage,the combination of the tug and the debris flies unpowered and uncontrolled to a swing point on the transfer orbit.Finally,in the third stage,the tug is propelled at the swing point and the rotation speed of the tethered system increases such that the debris obtains enough velocity increment.The trajectory optimization of the first stage is established considering the total fuel consumption of the three stages,whereas the dynamic model is simplified for computation efficiency.The solution to the optimal problem is obtained using a direct method based on Gauss pesudospectral discretization.Then a model predictive controller is designed to track the open-loop optimal reference trajectories,reducing the states’deviations caused by model simplification and ignorance of perturbations.Furthermore,it is proved that the fuel-optimal swing point is the apogee of the transfer orbit.The paper analyzes the fuel consumption of a typical scenario and demonstrates effectiveness of the proposed deorbit scheme numerically.展开更多
The fuel-optimal transfer trajectories using solar electric propulsion are designed considering the power constraints and solar array performance degradation.Three different performance degradation models including li...The fuel-optimal transfer trajectories using solar electric propulsion are designed considering the power constraints and solar array performance degradation.Three different performance degradation models including linear,positive and negative exponential degradations are used in the analysis of three typical rendezvous missions including Apophis,Venus and Ceres,respectively.The optimal control problem is formulated using the calculus of variations and Pontryagin’s maximum principle,which leads to a bang-bang control that is solved by indirect method combined with a homotopic technique.In demonstrating the effects of the power constraints and solar array performance degradation on the power budget and fuel consumption,the time histories of the power profile and the fuel consumptions are compared for the three missions.This study indicates that it is necessary to consider the power constraints and solar array performance degradation for the SEP-based low-thrust trajectory design,espacially for long-duration outbound flights.展开更多
Station-keeping(SK) is indispensable in actual geostationary(GEO) satellite missions. Due to the luni-solar gravity perturbations, the inclination of a GEO satellite suffers the issues of secular drift and long-period...Station-keeping(SK) is indispensable in actual geostationary(GEO) satellite missions. Due to the luni-solar gravity perturbations, the inclination of a GEO satellite suffers the issues of secular drift and long-period oscillation. Current north-south(NS)SK strategies maintain the GEO satellite’s orbit with high accuracy but low fuel efficiency. In this work, an efficient highaccuracy NS-SK strategy is developed for the GEO satellites. First, an averaging method is employed to decrease the accumulation of the secular drift within a one-solar-day SK cycle, while the long-period oscillation caused by the solar gravity is damped to further improve the orbital accuracy using the impulse and finite-thrust propulsions. Second, we contribute a fueloptimal cycle that reduces the fuel consumption and a fixed-interval cycle that executes SK control in fixed time interval every day to further enhance the proposed NS-SK strategy. Numerical simulations show that the improved strategy can achieve highaccuracy NS-SK with little fuel consumption. Moreover, results also demonstrate that the fixed-interval cycle can reach higher NS-SK accuracy while consuming less fuel.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grants Nos.11672146 and 11432001).
文摘In this study,a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing problem.Considering the remote communication restrictions and environmental uncertainties,advanced landing control techniques are demanded to meet the high requirements of real-time performance and autonomy in the Moon landing missions.Deep reinforcement learning(DRL)algorithms have been recently developed for real-time optimal control but suffer the obstacles of slow convergence and difficult reward function design.To address these problems,a DRL algorithm is developed using an actor-indirect method architecture to achieve the optimal control of the Moon landing mission.In this DRL algorithm,an indirect method is employed to generate the optimal control actions for the deep neural network(DNN)learning,while the trained DNNs provide good initial guesses for the indirect method to promote the efficiency of training data generation.Through sufficient learning of the state-action relationship,the trained DNNs can approximate the optimal actions and steer the spacecraft to the target in real time.Additionally,a nonlinear feedback controller is developed to improve the terminal landing accuracy.Numerical simulations are given to verify the effectiveness of the proposed DRL algorithm and demonstrate the performance of the developed optimal landing controller.
基金supported by the National Natural Science Foundation of China(Nos.11872223,11902174,11772167)。
文摘Traditionally,numerical trajectory integration for shooting equation calculation and iterations for shooting with randomly guessed initial solutions deteriorate the real-time performance of indirect methods for on-board applications.In this study,the indirect method is improved to achieve real-time trajectory optimization of fuel-optimal powered planetary landings with the help of analytical shooting equation derivations and a practical homotopy technique.Specifically,the contributions of this paper are threefold.First,the analytical expressions for shooting equation calculation are derived to replace the traditional time-consuming trajectory integration.Consequently,the computational efficiency is significantly improved.Second,the original three-dimensional landing problem is connected with a simplified one-dimensional problem that only involves the vertical dynamics,and its analytical solution is obtained based on Pontryagin’s minimum principle.Third,starting with the analytical solution,the accurate solution of the original landing problem can be obtained through an adaptive homotopy process.Simulation results of Earth landing scenarios are given to substantiate the effectiveness of the proposed techniques and illustrate that the developed method can obtain a fuel-optimal landing trajectory in 5 ms with 100%success rate.
基金supported by the National Natural Science Foundation of China(No.11772023)。
文摘This paper proposes a fuel-optimal deorbit scheme for space debris deorbit using tethered space tug.The scheme contains three stages named respectively as dragging,maintenance and swinging.In the first stage,the tug,propelled by continuous thrust,tows deorbit to a transfer orbit with a tether.Then in the second stage,the combination of the tug and the debris flies unpowered and uncontrolled to a swing point on the transfer orbit.Finally,in the third stage,the tug is propelled at the swing point and the rotation speed of the tethered system increases such that the debris obtains enough velocity increment.The trajectory optimization of the first stage is established considering the total fuel consumption of the three stages,whereas the dynamic model is simplified for computation efficiency.The solution to the optimal problem is obtained using a direct method based on Gauss pesudospectral discretization.Then a model predictive controller is designed to track the open-loop optimal reference trajectories,reducing the states’deviations caused by model simplification and ignorance of perturbations.Furthermore,it is proved that the fuel-optimal swing point is the apogee of the transfer orbit.The paper analyzes the fuel consumption of a typical scenario and demonstrates effectiveness of the proposed deorbit scheme numerically.
基金supported by National Basic Research Program of China (Grant No. 2012CB720000)the Fund of Science and Technology on Aerospace Flight Dynamic Laboratory (Grant No. 2012AFDL006)
文摘The fuel-optimal transfer trajectories using solar electric propulsion are designed considering the power constraints and solar array performance degradation.Three different performance degradation models including linear,positive and negative exponential degradations are used in the analysis of three typical rendezvous missions including Apophis,Venus and Ceres,respectively.The optimal control problem is formulated using the calculus of variations and Pontryagin’s maximum principle,which leads to a bang-bang control that is solved by indirect method combined with a homotopic technique.In demonstrating the effects of the power constraints and solar array performance degradation on the power budget and fuel consumption,the time histories of the power profile and the fuel consumptions are compared for the three missions.This study indicates that it is necessary to consider the power constraints and solar array performance degradation for the SEP-based low-thrust trajectory design,espacially for long-duration outbound flights.
基金supported by the National Natural Science Foundation of China(Grant No.61273051)Qing Lan Projectthe Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics(NUAA)(Grant No.BCXJ19-12)。
文摘Station-keeping(SK) is indispensable in actual geostationary(GEO) satellite missions. Due to the luni-solar gravity perturbations, the inclination of a GEO satellite suffers the issues of secular drift and long-period oscillation. Current north-south(NS)SK strategies maintain the GEO satellite’s orbit with high accuracy but low fuel efficiency. In this work, an efficient highaccuracy NS-SK strategy is developed for the GEO satellites. First, an averaging method is employed to decrease the accumulation of the secular drift within a one-solar-day SK cycle, while the long-period oscillation caused by the solar gravity is damped to further improve the orbital accuracy using the impulse and finite-thrust propulsions. Second, we contribute a fueloptimal cycle that reduces the fuel consumption and a fixed-interval cycle that executes SK control in fixed time interval every day to further enhance the proposed NS-SK strategy. Numerical simulations show that the improved strategy can achieve highaccuracy NS-SK with little fuel consumption. Moreover, results also demonstrate that the fixed-interval cycle can reach higher NS-SK accuracy while consuming less fuel.
