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Cooperative rendezvous between two spacecraft under finite thrust

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Abstract

Dynamic equations of orbital elements of a modified vernal equinox for a far-distance cooperative rendezvous between two spacecraft were set up in this paper. The process of the far-distance cooperative rendezvous was optimized by a hybrid algorithm combining particle swarm optimization and differential evolution. The convergent costate vectors were obtained and set as the initial values of sequential quadratic programming to search for precise solutions, and the results proved to be stable and convergent. It can be seen from the results that the flight time of the cooperative rendezvous would be largely saved the amplitude of the thrust would be increased if the other conditions are fixed, and the fuel consumption would not be increased. However, the flight time would no longer decrease when the amplitude of the thrust reaches a certain value. In the last section of this paper, cooperative rendezvous and active–passive rendezvous were compared and analyzed, showing the advantages of cooperative rendezvous when the initial conditions are the same.

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Abbreviations

\(a\) :

Semi-major axis

e :

Eccentricity

\(i\) :

Orbit inclination angle

\(I_{\text{sp}}\) :

Thruster-specific impulse

\(J\) :

Performance index

\(m_{0}\) :

Initial mass of the satellite

\(m\) :

Mass of the satellite

T :

Thrust

\(R_{\text{e}}\) :

Equator radius

\(u\) :

Ratio of the amplitude of the actual thrust relative to \(T_{\text{max} }\)

\(\varvec{\alpha}\) :

Unit direction vector

\(\beta\) :

Pitch angle

\(\theta\) :

True anomaly

\(\varvec{\varPhi}\) :

Shooting equation

\(\gamma\) :

Yaw angle

λ :

Costate

μ :

Gravitational constant of the earth

ω :

Perigee amplitude

Ω :

Longitude ascending node

g 0 :

Gravitational acceleration

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shandong University, 17923 Jingshi Road, Jinan, 250061, China

    Weiming Feng, Biao Wang, Kun Yang & Di Zhao

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  1. Weiming Feng
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  2. Biao Wang
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  3. Kun Yang
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  4. Di Zhao
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Correspondence to Weiming Feng.

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Feng, W., Wang, B., Yang, K. et al. Cooperative rendezvous between two spacecraft under finite thrust. CEAS Space J 9, 227–241 (2017). https://doi.org/10.1007/s12567-017-0145-9

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  • DOI: https://doi.org/10.1007/s12567-017-0145-9

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