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
A new orbit transfer method is presented by combining the genetic algorithm（GA）with the refined Q-law method.Considering the energy consumption,the relative thrust efficiency is introduced as a threshold deciding wh...A new orbit transfer method is presented by combining the genetic algorithm（GA）with the refined Q-law method.Considering the energy consumption,the relative thrust efficiency is introduced as a threshold deciding whether to thrust or coast.GA is used to achieve the global time-optimal orbit transfer.The trajectory optimization problem is transformed into the constraint parameter optimization problem,thus the nonlinear two-point boundary value problem is avoided.The refined Q-law method integrated with the fuzzy logic control is adopted for the end course,the vibration is avoided and the high precision is achieved.The numerical simulation of satellite orbit transfer is implemented.Results show that the new method can achieve the time-optimal orbit transfer and the low energy consumption,thus improving the transfer precision.展开更多
Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method t...Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.展开更多
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
A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits(SS...A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits(SSO).The solving methodology proceeds in two steps:Firstly,the variance of the right ascension of ascending node(RAAN)of the debris group is used for narrowing down the potential debris candidate;secondly,the debris of the candidate group that has closest RAAN to the current debris is chosen as the next debris.The low thrust near-minimum-fuel trajectories of each rendezvous leg are obtained by the indirect optimization method.The proposed approach is demonstrated for the problem of the 8th China Trajectory Optimization Competition(CTOC).The radar cross section(RCS)of the debris is also considered in the first step since the primary performance index of the competition is to maximize the total RCS of the debris visited.The results show that the proposed approach achieves better performance within a competition period.Of the many rendezvous sequences found,the best one submitted for the competition obtained a total RCS of 184 by accomplishing rendezvous with 70 debris within a transfer duration of one year.展开更多
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 low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject ...The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.展开更多
Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates ...Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission.For the problem of global trajectory optimization,even with recent advances in low-thrust trajectory optimization,a full enumeration of this problem is not possible.This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions.The flight sequence is determined in ballistic scenario,and a differential evolution method is used with constructing a three-impulse transfer problem,then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories.The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.展开更多
This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium point...This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.展开更多
Conjunctions between spacecraft are increasingly common across orbital regimes,demanding reliable and efficient collision avoidance(COLA)strategies.The typical solution to the COLA problem is to compute a maneuver tha...Conjunctions between spacecraft are increasingly common across orbital regimes,demanding reliable and efficient collision avoidance(COLA)strategies.The typical solution to the COLA problem is to compute a maneuver that reduces the collision risk while minimizing fuel expenditure.If the spacecraft is in a continuously propelled phase,this approach must be modi ed since the thrust pro le is determined a priori,aiming to reach a nal orbit.This work proposes using convex optimization to solve the short-term encounter COLA problem in such conditions.The optimization problem is two-fold:(i)the collision risk must be reduced below a certain threshold;(ii)after the conjunction,the spacecraft must be rerouted into the nominal trajectory.By casting the problem as a sequential convex program,the original nonlinear optimal control problem is solved iteratively,recovering an optimal solution.Within the second-order cone program framework,three strategies are proposed to address the problem:(i)determining the optimal switch-o time to avoid the collision while minimizing deviation from the nominal trajectory;computing a new thrust pro le,deviating as little as possible from the original one in terms of(ii)vector or(iii)angular di erence.The three strategies are tested on practical operational scenarios,using the nominal thrust pro le from a low-thrust geostationary transfer orbit and conjunction details from a conjunction data message.展开更多
This article presents a systematic direct approach to carry out effective optimization of a wide range of continuous-thrust Earth-orbit transfers with intermediate-level thrust acceleration,including minimum-time (wit...This article presents a systematic direct approach to carry out effective optimization of a wide range of continuous-thrust Earth-orbit transfers with intermediate-level thrust acceleration,including minimum-time (with a single burn arc) and mini-mum-fuel (with multiple burn arcs) transfers. With direct control parameterization,in which the control steering programs of burn arcs are interpolated through a finite number of nodes,the optimal control problem is converted into the parameter optimi-zation proble...展开更多
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 Key Project of Natural Science Foundation of Jiangsu Province(BK2010072)~~
文摘A new orbit transfer method is presented by combining the genetic algorithm（GA）with the refined Q-law method.Considering the energy consumption,the relative thrust efficiency is introduced as a threshold deciding whether to thrust or coast.GA is used to achieve the global time-optimal orbit transfer.The trajectory optimization problem is transformed into the constraint parameter optimization problem,thus the nonlinear two-point boundary value problem is avoided.The refined Q-law method integrated with the fuzzy logic control is adopted for the end course,the vibration is avoided and the high precision is achieved.The numerical simulation of satellite orbit transfer is implemented.Results show that the new method can achieve the time-optimal orbit transfer and the low energy consumption,thus improving the transfer precision.
基金National Natural Science Foundation of China (10603005)
文摘Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.
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We are very grateful to the organizers of the 8th China Trajectory Optimization Competition for the interesting and complex problemMost methods presented in this paper were developed under the National Natural Science Foundation of China(Nos.11172036,11572037,and 11402021)the Excellent Young Scholars Research Fund of Beijing Institute of Technology(No.2015YG0101).
文摘A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits(SSO).The solving methodology proceeds in two steps:Firstly,the variance of the right ascension of ascending node(RAAN)of the debris group is used for narrowing down the potential debris candidate;secondly,the debris of the candidate group that has closest RAAN to the current debris is chosen as the next debris.The low thrust near-minimum-fuel trajectories of each rendezvous leg are obtained by the indirect optimization method.The proposed approach is demonstrated for the problem of the 8th China Trajectory Optimization Competition(CTOC).The radar cross section(RCS)of the debris is also considered in the first step since the primary performance index of the competition is to maximize the total RCS of the debris visited.The results show that the proposed approach achieves better performance within a competition period.Of the many rendezvous sequences found,the best one submitted for the competition obtained a total RCS of 184 by accomplishing rendezvous with 70 debris within a transfer duration of one year.
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 low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.
文摘Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission.For the problem of global trajectory optimization,even with recent advances in low-thrust trajectory optimization,a full enumeration of this problem is not possible.This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions.The flight sequence is determined in ballistic scenario,and a differential evolution method is used with constructing a three-impulse transfer problem,then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories.The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.
文摘This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.
基金supported by the Air Force Office of Scientific Research under award number FA2386-21-1-4115.
文摘Conjunctions between spacecraft are increasingly common across orbital regimes,demanding reliable and efficient collision avoidance(COLA)strategies.The typical solution to the COLA problem is to compute a maneuver that reduces the collision risk while minimizing fuel expenditure.If the spacecraft is in a continuously propelled phase,this approach must be modi ed since the thrust pro le is determined a priori,aiming to reach a nal orbit.This work proposes using convex optimization to solve the short-term encounter COLA problem in such conditions.The optimization problem is two-fold:(i)the collision risk must be reduced below a certain threshold;(ii)after the conjunction,the spacecraft must be rerouted into the nominal trajectory.By casting the problem as a sequential convex program,the original nonlinear optimal control problem is solved iteratively,recovering an optimal solution.Within the second-order cone program framework,three strategies are proposed to address the problem:(i)determining the optimal switch-o time to avoid the collision while minimizing deviation from the nominal trajectory;computing a new thrust pro le,deviating as little as possible from the original one in terms of(ii)vector or(iii)angular di erence.The three strategies are tested on practical operational scenarios,using the nominal thrust pro le from a low-thrust geostationary transfer orbit and conjunction details from a conjunction data message.
基金National Natural Science Foundation of China (10603005)Foundation of President of the Academy of Opto-Electro-nics ( AOE-CX-200601)
文摘This article presents a systematic direct approach to carry out effective optimization of a wide range of continuous-thrust Earth-orbit transfers with intermediate-level thrust acceleration,including minimum-time (with a single burn arc) and mini-mum-fuel (with multiple burn arcs) transfers. With direct control parameterization,in which the control steering programs of burn arcs are interpolated through a finite number of nodes,the optimal control problem is converted into the parameter optimi-zation proble...
