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Synthesis of Optimal Control Program of Spacecraft Attitude Taking into Account Energy of Rotation

American Journal of Mathematical and Computational Sciences
Vol.4 , No. 2, Publication Date: Aug. 22, 2019, Page: 24-36

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Authors

[1]	Mikhail Valer’evich Levskii, Research Institute of Space Systems, Khrunichev State Space Research-and-Production Center, Korolev, Russia.

Abstract

The solving the original dynamical control problem of optimal reorientation from a state of rest to a state of rest is investigated. The control function is torque vector. The case, when control is limited and the used functional takes into account kinetic rotation energy and time of maneuver, is studied in detail. For designing the optimal control program, the quaternion method and the Pontryagin’s maximum principle are used. Analytic solution of the proposed problem is presented basing on the differential equation connecting the angular velocity vector and quaternion of spacecraft attitude. It is shown that the chosen criterion of quality provides a turn of a spacecraft with rotation energy which do not exceed the required value. This property of the proposed control increases safety of flight. All key expressions and equations are written in quaternion form which is convenient for onboard realization and implementation. Analytical formulas were written for duration of acceleration and braking. For specific cases of spacecraft’s configurations (dynamically symmetric and spheric-symmetrical spacecraft as particular cases), complete solution of optimal control problem in closed form is given. Numerical example and results of mathematical simulation for spacecraft motion under optimal control are demonstrated. This data supplements the made theoretical descriptions, and illustrates reorientation process in visual form.

Keywords

Rotation Maneuver, Quaternion of Attitude, Optimal Control Problem, Criterion of Quality, Maximum Principle

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