Optimal Control of the Spacecraft Relative Motion on Near-Circular Orbits with Limitations on the Thrust Direction

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 in a near-circular orbit with limitation on the of the thrust vector orientation.

New variables describing the relative motion in the orbital plane in terms of secular and periodic motion and in lateral plane in the form of the amplitude and phase of of the maneuvering spacecraft oscillations relative to the passive one were obtained based on the equations of motion in the orbital cylindrical reference frame.

Limitations on possible orientation of the thrust vector that can be oriented in the plane of local horizon, which is important for the spacecraft with tight fixation of the propulsion system onboard, were introduced. Thus, in the case under consideration the spacecraft should be rotated only in one plane, which is certainly will simplify the motion control system of equations as well as the spacecraft orientation system of equations.

The time optimal control modes were obtained employing the Pontryagin maximum principle, while optimization problem was reduced to the two-point boundary value problem for the system of differential equations, which is solved for several qualitatively different boundary conditions, namely  domination of correction of longitudinal secular motion  as well as domination of the lateral motion correction requirement.

The article demonstrates that limitations introduction on the thrust vector orientation allowed obtaining more stepless aircraft control program (program of rotation). However, as the computations revealed, amplitude of the necessary angles became larger than with the option of control without thrust orientation limitations.

Comparison of the considered control with limitation with the optimal one without limitation was performed for the introduced boundary conditions, which revealed that the greatest degree of non-optimality (relative motion duration increment) was accounted for cases of the domination of the periodic motion correction requirement, irrespective of whether this motion was lateral or longitudinal.

Simulation of the optimal control, obtained with a linear model of relative motion, was performed with the original non-linearized model of motion with the osculating elements. The article demonstrates that in the case of relatively small initial distances between the spaceships, linearization practically did not affect on the accuracy of bringing the spacecraft to a set position. With the initial distance between the spacecraft increasing to 30 degrees and above this value, the inference can be drawn that the obtained control does not lead the maneuvering spacecraft to a given relative position.

Keywords:

spacecraft relative motion control, orbital cylindrical reference frame, dimensionless parameters of relative motion, secular and periodic components of motion, thrust orientation in the local horizon plane

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