Shape-Based Approximation of Constrained Low-Thrust Space Trajectories Using Fourier Series

2012 ◽  
Vol 49 (3) ◽  
pp. 535-545 ◽  
Author(s):  
Ehsan Taheri ◽  
Ossama Abdelkhalik
Keyword(s):  
Fourier Series ◽  
Low Thrust ◽  
Space Trajectories

Approximate On-Off Low-Thrust Space Trajectories Using Fourier Series

2012 ◽  
Vol 49 (5) ◽  
pp. 962-965 ◽  
Author(s):  
Ossama Abdelkhalik ◽  
Elsan Taheri
Keyword(s):  
Fourier Series ◽  
Low Thrust ◽  
Space Trajectories

Analytical Space Trajectories for Extremal Motion with Low-Thrust Exhaust-Modulated Propulsion

2001 ◽  
Vol 38 (6) ◽  
pp. 897-903 ◽  
Author(s):  
Robert H. Bishop ◽  
Dilmurat M. Azimov
Keyword(s):  
Low Thrust ◽  
Space Trajectories

Initial design of low-thrust trajectories based on the Bezier curve-based shaping approach

2020 ◽  
Vol 234 (11) ◽  
pp. 1825-1835
Author(s):  
Zichen Fan ◽  
Mingying Huo ◽  
Naiming Qi ◽  
Ce Zhao ◽  
Ze Yu ◽  
...  
Keyword(s):  
Fourier Series ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Mission Design ◽  
Bézier Curve ◽  
Design Stage ◽  
Bezier Curve ◽  
Series Method ◽  
Low Thrust ◽  
Fourier Series Method

This paper presents a method to use the Bezier curve to rapidly generate three-dimensional low-thrust trajectories, which can provide a suitable initial approximation to be used for more accurate trajectory optimal control tools. Two missions, from Earth to Mars and the asteroid Dionysus, are considered to evaluate the performance of the method. In order to verify the advantages of this method, it is compared with the finite Fourier series method. Numerical results show that the Bezier method can get better performance index in shorter computation time compared with the finite Fourier series method. The applicability of the solution obtained by Bezier method is evaluated by introducing the obtained solution into the Gauss pseudospectral method as an initial guess. The simulation results show that the Bezier method can rapidly generate a very suitable three-dimensional initial trajectory for the optimal solver. This is very important for rapid evaluation of the feasibility of a large number of low-thrust flight schemes in the preliminary mission design stage.

scholarly journals Low-Thrust Trajectory Design Using Finite Fourier Series Approximation of Pseudoequinoctial Elements

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Wanmeng Zhou ◽  
Haiyang Li ◽  
Hua Wang ◽  
Ran Ding
Keyword(s):  
Fourier Series ◽  
Inverse Dynamics ◽  
Design Method ◽  
Momentum Conservation ◽  
Trajectory Design ◽  
Series Method ◽  
Low Thrust ◽  
Control Variables ◽  
Inverse Simulation ◽  
Fourier Series Method

A new low-thrust trajectory design method is proposed that is based on the finite Fourier series method with pseudoequinoctial elements rather than the more common cylindrical coordinate components. The bijection relation between the elements and control variables is ensured by introducing an additional equality constraint derived from the angular momentum conservation. The guidance law and on-line control variables are obtained by applying inverse dynamics and the framework of inverse simulation technology, respectively. The pseudoequinoctial finite Fourier series method has the advantages of both the Fourier series and the perturbation analysis methods. For two-body problems, three cases were studied: the Earth to Mars, 1989ML, and Tempel-1 missions. Regarding the design of a rendezvous trajectory with a large inclination angle and a high eccentricity rate, this method yields a broader range of feasible results than the traditional Fourier series method. The circular restricted three-body problem was solved for the first time using the pseudoequinoctial finite Fourier series method combined with the patched conics method. The low-thrust Earth-Moon transfer was analyzed, and the results show that this method improves window analysis efficiency and guarantees precision of the initial geocentric trajectory for the low-thrust transfer.

scholarly journals A Shape-Based Method for Continuous Low-Thrust Trajectory Design between Circular Coplanar Orbits

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Qun Fang ◽  
Xuefeng Wang ◽  
Chong Sun ◽  
Jianping Yuan
Keyword(s):  
Fourier Series ◽  
Trajectory Optimization ◽  
Lower Cost ◽  
Necessary Conditions ◽  
Trajectory Design ◽  
Low Thrust ◽  
First Order ◽  
The Earth ◽  
Free Case ◽  
Preliminary Phase

The shape-based method can provide suitable initial guesses for trajectory optimization, which are useful for quickly converging a more accurate trajectory. Combined with the optimal control theory, an optimized shape-based method using the finite Fourier series is proposed in this paper. Taking the flight time-fixed case and the time-free case into account, respectively, the optimized shape-based method, which considers the first-order optimal necessary conditions, can guarantee that not only an orbit designed during the preliminary phase is optimal, but also the thrust direction is not constrained to be tangential. Besides, the traditional shape-based method using the finite Fourier series, in which the thrust direction is constrained to be tangential, is developed for the time-free case in this paper. The Earth-Mars case and the LEO-GEO case are used to verify the optimized shape-based method’s feasibility for time-fixed and time-free continuous low-thrust trajectory design between circular coplanar orbits, respectively. The optimized shaped-based method can design a lower cost trajectory.

A multi-objective approach to the design of low thrust space trajectories using optimal control

2009 ◽  
Vol 105 (1-3) ◽  
pp. 33-59 ◽  
Author(s):  
Michael Dellnitz ◽  
Sina Ober-Blöbaum ◽  
Marcus Post ◽  
Oliver Schütze ◽  
Bianca Thiere
Keyword(s):  
Optimal Control ◽  
Low Thrust ◽  
Space Trajectories ◽  
Multi Objective

Rendez vous with Saturn's rings

1984 ◽  
Vol 75 ◽  
pp. 743-759 ◽  
Author(s):  
Kerry T. Nock
Keyword(s):  
Solar Energy ◽  
Electric Propulsion ◽  
Power Source ◽  
Propulsion System ◽  
Low Thrust ◽  
Ring Plane ◽  
The Earth ◽  
Total Impulse ◽  
Saturn's Rings

ABSTRACTA mission to rendezvous with the rings of Saturn is studied with regard to science rationale and instrumentation and engineering feasibility and design. Future detailedin situexploration of the rings of Saturn will require spacecraft systems with enormous propulsive capability. NASA is currently studying the critical technologies for just such a system, called Nuclear Electric Propulsion (NEP). Electric propulsion is the only technology which can effectively provide the required total impulse for this demanding mission. Furthermore, the power source must be nuclear because the solar energy reaching Saturn is only 1% of that at the Earth. An important aspect of this mission is the ability of the low thrust propulsion system to continuously boost the spacecraft above the ring plane as it spirals in toward Saturn, thus enabling scientific measurements of ring particles from only a few kilometers.

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