Optimal control of spacecraft relative motion by the response rate criterion on near-circular orbits

Aeronautical and Space-Rocket Engineering


Аuthors

Chou X. *, Ishkov S. A.**, Filippov G. A.***

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: chousyao@yandex.ru
**e-mail: ishkovs@gmail.com
***e-mail: filippov.ga@ssau.ru

Abstract

The article presents the study of optimal control programs for spatial relative motion at near-circular orbit.

Two spacecraft, namely maneuvering, equipped with engine of finite thrust, and passive, located in a circular orbit are being considered.

The problem of bringing the maneuvering spacecraft to the specified position relative to the passive one is being set. Equations in cylindrical reference frame, which origin is placed in center of mass of the passive aircraft, and equations of motion are linearized near the passive spacecraft orbit, are used for construction of the dimensionless and invariant to the datum orbit mathematical model of relative motion.

New variables, describing the relative motion in the orbit plane in terms of the secular and periodical motion, and in the form of the maneuvering spacecraft oscillations amplitude and phase relative to the passive one, are introduced.

The authors demonstrate that longitudinal motion in linear approximation is associated with the lateral one only through the controlling accelerations, in which connection two control options are considered. The first one is joint, when both longitudinal and lateral motion components change simultaneously, and no limitations are imposed herewith on the thrust vector orientation of the maneuvering spacecraft. The second one, which is no less common, supposes sequential longitudinal component elimination of the relative motion, and then the lateral one.

Time optimal controls are obtained with the Pontryagin maximum principle application. The optimization problem is reduced to a two-point boundary problem for a system of differential equations, which is solved for three qualitatively different boundary conditions, namely the longitudinal periodic motion correction dominance, the requirements of longitudinal secular motion correction and the requirements of the lateral motion correction dominance.

An additional calculation of the required turning speed of the active spacecraft was performed to the optimal control program accomplishment, which indicated the necessity of introducing the passive sections on the trajectory at time instants corresponding to an almost instantaneous turn of the spacecraft by one hundred and eighty degrees around its axis.

Keywords:

relative motion of spacecraft, orbital cylindrical reference frame, dimensionless parameters of motion, longitudinal and lateral motion, secular and periodic motion components, control with free orientation of thrust

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