Analytical Solution for Power-Limited Optimal Rendezvous near an Elliptic Orbit |
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Authors: | P Sengupta S R Vadali |
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Institution: | (1) Department of Aerospace Engineering, MS 3141, Texas A&M University, College Station, TX 77843-3141, USA |
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Abstract: | This paper presents an analytical solution to the problem of the optimal rendezvous using power-limited propulsion for a spacecraft
in an elliptic orbit in a gravitational field. The derivation of the result assumes small relative distances, but does not
make any assumption on the eccentricity of the orbit and does not require numerical integration. The results are generalized
to include the possibility of different weights on the control effort for each axis (radial, along-track, and out-of-plane).
When the weights on the control efforts are unequal, several integrals are used whose solutions may be represented by infinite
series in a small parameter dependent on the eccentricity. A methodology is introduced where the series can be extended trivially
to as many terms as desired. Furthermore, for a given numerical tolerance, an upper bound on the number of terms required
to represent the series is also obtained. When the weights are equal for all the three axes, the series representations are
no longer necessary. The results can be used easily to design optimal feedback controls for rendezvous maneuvers, or for generating
initial guesses for two-point boundary-value problems for numerical solutions to the nonlinear rendezvous problem. |
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Keywords: | Optimal rendezvous Power-limited propulsion Eccentric orbits Tschauner-Hempel equations Lambert W function |
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