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Optimal Control for a Cooperative Rendezvous Between Two Spacecraft from Determined Orbits

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Abstract

The mathematical model of a far-distance cooperative rendezvous between two spacecraft in a non-Keplerian orbit was established. Approximate global optimization was performed by a type of hybrid algorithm consisting of particle swarm optimization and differential evolution. In this process, the double-fitness function was established according to the objective function and the constraints; the double-fitness function was used to enable a better choice between the solutions obtained by the two algorithms at every iteration. In addition, the costate variables obtained were set as the initial values of the sequential quadratic programming to greatly increase the possibility of finding the approximate global optimal solution. After performing the calculations and simulations, it was concluded that the fuel required for orbiting was not influenced by the initial positions of the two spacecraft if the initial orbits of the two spacecraft were determined. However, the time consumption is strongly influenced in this situation.

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Abbreviations

a :

semimajor axis

e :

eccentricity

i :

orbit inclination angle

I sp :

thruster-specific impulse

J :

performance index

m 0 :

initial mass of the satellite

R e :

equator radius

u :

ratio of the amplitude of the actual thrust relative to T max

α :

unit direction vector

β :

pitch angle

θ :

true anomaly

Φ :

shooting equation

γ :

yaw angle

λ :

costate

μ :

gravitational constant of the earth

ω :

perigee amplitude

Ω:

longitude ascending node

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shandong University, Jinan, 260062, China

    Weiming Feng, Liping Han, Di Zhao & Kun Yang

  2. Department of Mechanical Engineering & Materials Science, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Lei Shi

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  1. Weiming Feng
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  2. Liping Han
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  4. Di Zhao
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  5. Kun Yang
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Correspondence to Weiming Feng.

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Feng, W., Han, L., Shi, L. et al. Optimal Control for a Cooperative Rendezvous Between Two Spacecraft from Determined Orbits. J of Astronaut Sci 63, 23–46 (2016). https://doi.org/10.1007/s40295-015-0079-4

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