scholarly journals Homotopy method for minimum consumption orbit transfer problem

2006 ◽  
Vol 12 (2) ◽  
pp. 294-310 ◽  
Author(s):  
Joseph Gergaud ◽  
Thomas Haberkorn
Keyword(s):  
Transfer Problem ◽  
Homotopy Method ◽  
Orbit Transfer

scholarly journals Algebraic Approach to the Minimum-Cost Multi-Impulse Orbit-Transfer Problem

2016 ◽  
Vol 39 (8) ◽  
pp. 1734-1743 ◽  
Author(s):  
M. Avendaño ◽  
V. Martín-Molina ◽  
J. Martín-Morales ◽  
J. Ortigas-Galindo
Keyword(s):  
Transfer Problem ◽  
Algebraic Approach ◽  
Minimum Cost ◽  
Orbit Transfer

A quadratic homotopy method for fuel-optimal low-thrust trajectory design

2018 ◽  
Vol 233 (5) ◽  
pp. 1741-1757 ◽  
Author(s):  
Binfeng Pan ◽  
Xun Pan ◽  
Yangyang Ma
Keyword(s):  
Trajectory Optimization ◽  
Transfer Problem ◽  
Quadratic Function ◽  
Homotopy Method ◽  
Linear Functions ◽  
Optimal Controls ◽  
Homotopy Methods ◽  
Low Thrust ◽  
Starting Point ◽  
Rendezvous Problem

Solving fuel-optimal low-thrust trajectory problems is a long-standing challenging topic, mainly due to the existence of discontinuous bang–bang controls and small convergence domain. Homotopy methods, the principle of which is to embed a given problem into a family of problems parameterized by a homotopic parameter, have been widely applied to address this difficulty. Linear homotopy methods, the homotopy functions of which are linear functions of the homotopic parameter, serve as useful tools to provide continuous optimal controls during the homotopic procedure with an energy-optimal low-thrust trajectory optimization problem as the starting point. However, solving energy-optimal problem is still not an easy task, particularly for the low-thrust orbital transfers with many revolutions or asteroids flyby, which is typically solved by other advanced numerical optimization algorithms or other homotopy methods. In this paper, a novel quadratic homotopy method, the homotopy function of which is a quadratic function of the homotopic parameter, is presented to circumvent this possible difficulty of solving the initial problem in the existing linear homotopy methods. A fixed-time full-thrust problem is constructed as the starting point of this proposed quadratic homotopy, the analytical solution of which can be easily obtained under a modified linear gravity approximation formulation. The criterion of energy-optimal problem is still involved in the homotopic procedure to provide continuous optimal controls until the original fuel-optimal problem is solved. Numerical demonstrations in an Earth to Venus rendezvous problem, a geostationary transfer orbit (GTO) to geosynchronous orbit (GEO) orbital transfer problem with many revolutions, and an Earth to Mars rendezvous problem with an asteroid flyby are presented to illustrate the applications of this proposed homotopy method.

Study of Henon's orbit transfer problem using the Lambert algorithm

1994 ◽  
Vol 17 (5) ◽  
pp. 1075-1081 ◽  
Author(s):  
Antonio F. B. A. Prado ◽  
Roger A. Broucke
Keyword(s):  
Transfer Problem ◽  
Orbit Transfer

scholarly journals Solving Coplanar Power-Limited Orbit Transfer Problem by Primer Vector Approximation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Weijun Huang
Keyword(s):  
Vector Function ◽  
Approximation Method ◽  
Transfer Problem ◽  
Approximate Solutions ◽  
Orbit Transfer ◽  
Numerical Tests ◽  
Vector Approximation ◽  
Primer Vector

The coplanar orbit transfer problem has been an important topic in astrodynamics since the beginning of the space era. Though many approximate solutions for power-limited orbit transfer problem have been developed, most of them rely on simplifications of the dynamics of the problem. This paper proposes a new approximation method called primer vector approximation method to solve the classic power-limited orbit transfer problem. This method makes no simplification on the dynamics, but instead approximates the optimal primer-vector function. With this method, this paper derives two approximate solutions for the power-limited orbit transfer problem. Numerical tests show the robustness and accuracy of the approximations.

Design and Optimization of Low-Thrust Orbit Transfers Using Hybrid Method

2012 ◽  
Vol 588-589 ◽  
pp. 335-339 ◽  
Author(s):  
Lei Fu ◽  
Min Xu ◽  
Xiao Min An ◽  
Xun Liang Yan
Keyword(s):  
Parametric Optimization ◽  
Transfer Problem ◽  
Hybrid Genetic Algorithm ◽  
Minimum Time ◽  
Reference Trajectory ◽  
Low Thrust ◽  
Orbit Transfer ◽  
Design And Optimization ◽  
Earth’S Oblateness ◽  
Thrust Allocation

A low-thrust guidance scheme, which is weighted combined by taking the optimum strategy of thrust allocation and the target deficits value into consideration for each orbital element, is developed. The presented guidance scheme is predictive in nature and does not rely on a stored reference trajectory or reference controls. The orbit transfer problem is converted into parametric optimization and utilizing a hybrid genetic algorithm. The minimum-time orbit transfer is considered. The influence of the Earth’s oblateness is taken into consideration in the simulation of minimum-time. A conclusion is drawn that the designed method presented here turns out to be an autonomous scheme because the information of target orbit is considered in the transfer process.

Multiple-Spacecraft Orbit-Transfer Problem: The No-Booster Case

1999 ◽  
Vol 22 (5) ◽  
pp. 650-657 ◽  
Author(s):  
Cesar A. Ocampo ◽  
George W. Rosborough
Keyword(s):  
Transfer Problem ◽  
Orbit Transfer ◽  
Spacecraft Orbit ◽  
Multiple Spacecraft
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