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2011, 1(3): 435-485. doi: 10.3934/naco.2011.1.435

Orbital transfers: optimization methods and recent results

1. 

Scuola di Ingegneria Aerospaziale -- University of Rome "La Sapienza", via Salaria 851, 00138 Rome, Italy

Received  April 2011 Revised  July 2011 Published  September 2011

A wide variety of techniques have been employed in the past for optimizing orbital transfers, which represent the trajectories that lead a spacecraft from a given initial orbit to a specified final orbit. This paper describes several original approaches to optimizing impulsive and finite--thrust orbital transfers, and presents some very recent results. First, impulsive transfers between Keplerian trajectories are considered. A new, analytical optimization method applied to these transfers leads to conclusions of a global nature for transfers involving both ellipses and escape trajectories, without any limitation on the number of impulses, and with possible constraints on the radius of closest approach and greatest recession from the attracting body. A direct optimization technique, termed direct collocation with nonlinear programming algorithm, is then applied to finite--thrust transfers between circular orbits. Lastly, low--thrust orbital transfers are optimized through the joint use of the necessary conditions for optimality and of the recently introduced heuristic method referred to as particle swarm optimization. This work offers a complete description and demonstrates the effectiveness of the distinct techniques applied to optimizing orbital transfer problems of different nature.
Citation: Mauro Pontani. Orbital transfers: optimization methods and recent results. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 435-485. doi: 10.3934/naco.2011.1.435
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show all references

References:
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P. J. Angeline, Evolutionary optimization versus particle swarm optimization: philosophy and performance Differences,, Evolutionary programming VII, 1447 (1998), 601.   Google Scholar

[2]

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[3]

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[4]

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[5]

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[6]

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[7]

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[8]

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[12]

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[18]

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[19]

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[20]

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[21]

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[23]

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[24]

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[25]

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[26]

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[27]

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[28]

P. C. Fourie and A. A. Groenwold, Particle swarms in topology optimization,, Proceedings of the Fourth World Congress of Structural and Multidisciplinary Optimization, (2001), 1771.   Google Scholar

[29]

P. C. Fourie and A. A. Groenwold, The particle swarm optimization algorithm in size and shape optimization,, Structural and Multidisciplinary Optimization, 23 (2002), 259.   Google Scholar

[30]

Y. Gao and and C. Kluever, Low-thrust interplanetary orbit transfer using hybrid trajectory optimization method with multiple shooting,, Paper AIAA 2004-5088 (2004)., (2004), 2004.   Google Scholar

[31]

D. E. Goldberg, "Genetic Algorithms in Search, Optimization, and Machine Learning,", Addison Wesley, (1989).   Google Scholar

[32]

C. R. Hargraves and S. W. Paris, Direct trajectory optimization using nonlinear programming and collocation,, Journal of Guidance, 10 (1987), 338.  doi: 10.2514/3.20223.  Google Scholar

[33]

R. Hassan, B. Cohanim and O. de Weck, Comparison of particle swarm optimization and the genetic algorithm,, Paper AIAA 2005-1897, (2005), 2005.   Google Scholar

[34]

G. A. Hazelrigg, Globally optimal impulsive transfers via Green's Theorem,, Journal of Guidance, 7 (1983), 462.  doi: 10.2514/3.19879.  Google Scholar

[35]

A. L. Herman and B. A. Conway, Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules,, Journal of Guidance, 19 (1996), 592.  doi: 10.2514/3.21662.  Google Scholar

[36]

A. L. Herman and B. A. Conway, Optimal low-thrust, earth-moon orbit transfer,, Journal of Guidance, 21 (1998), 141.  doi: 10.2514/2.4210.  Google Scholar

[37]

N. Higashi and H. Iba, Particle swarm optimization with Gaussian mutation,, Proceedings of the IEEE Swarm Intelligence Symposium (SIS 2003), (2003).   Google Scholar

[38]

F. B. Hildebrand, "Introduction to Numerical Analysis,", Dover, (1987).   Google Scholar

[39]

R. F. Hoelker and R. Silber, The bi-elliptical transfer between coplanar circular orbits,, Proceedings of the 4th Symposium on Ballistic Missiles and Space Technology, 3 (1961), 164.   Google Scholar

[40]

W. Hohmann, Die Erreichbarkeit der Himmelskoerper,, Oldenbourg, (1925).   Google Scholar

[41]

X. Hu and R. Eberhart, Solving constrained nonlinear optimization problems with particle swarm optimization,, Proceedings of the Sixth World Multiconference on Systemics, (2002).   Google Scholar

[42]

X. Hu, R. Eberhart and Y. Shi, Engineering optimization with particle swarm,, Proceedings of the IEEE Swarm Intelligence Symposium (SIS 2003), (2003).   Google Scholar

[43]

X. Hu, Y. Shi and R. Eberhart, Recent advances in particle swarm,, Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2004), (2004).   Google Scholar

[44]

M. R. Ilgen, Hybrid method for computing optimal low thrust OTV trajectories,, Advances in the Astronautical Sciences, 87 (1994), 941.   Google Scholar

[45]

M. R. Ilgen, Hybrid method for computing optimal low thrust OTV trajectories,, Advances in the Astronautical Sciences, 87 (1999), 941.   Google Scholar

[46]

A. B. Jenkin, Representative mission trade studies for low-thrust transfers to geosynchronous orbits,, paper AIAA 2004-5086 (2004)., (2004), 2004.   Google Scholar

[47]

V. Kalivarapu and E. Winer, Implementation of digital pheromones in particle swarm optimization for constrained optimization problems,, Paper AIAA 2008-1974 (2008)., (2008), 2008.   Google Scholar

[48]

J. A. Kechichian, Reformulation of Edelbaum's low-thrust transfer problem using optimal control theory,, Journal of Guidance, 20 (1997), 988.  doi: 10.2514/2.4145.  Google Scholar

[49]

J. A. Kechichian, Low-thrust eccentricity-constrained orbit raising,, Journal of Spacecraft and Rockets, 35 (1998), 327.  doi: 10.2514/2.3330.  Google Scholar

[50]

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