Analytical solution of the problem of optimal control of reorientation of solid body (spacecraft), in sense of a combined criteria of quality, based on the quaternions

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The problem on optimal reorientation of a solid (spacecraft) from an initial position into a prescribed final angular position on the basis of quaternions is solved. A combined criteria of quality is used, combining in a given proportion the contribution of control forces and the duration of maneuver, as well as the integral of the rotational energy. The synthesis of optimal control is based on a differential equation relating the attitude quaternion and angular momentum of a spacecraft. Analytical solution of optimal control problem is obtained using the necessary conditions of optimality in the form of the Pontryagin’s maximum principle. The properties of optimal rotation are studied in detail. Formalized equations and computational formulas are written to construct the optimal rotation program. Analytical equations and relations for finding the optimal control are presented. Key relations that determine the optimal values of the parameters of rotation control algorithm are given. A constructive scheme for solving the boundary-value problem of the maximum principle for arbitrary turning conditions (initial and final positions and moments of inertia of a solid) is given also. The made numerical experiments confirm the analytical conclusions. In the case of a dynamically symmetric solid body, the problem of spatial reorientation with minimum energy and time consumption is completely solved (in closed form). An example and results of mathematical modeling that confirm the practical feasibility of the developed method for orientation control are given.

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作者简介

M. Levskii

Maksimov Space System Research and Development Institute as branch of Khrunichev State Research and Production Space Center

编辑信件的主要联系方式.
Email: levskii1966@mail.ru
俄罗斯联邦, Korolev, Moscow oblast, 141091

参考

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2. Fig. 1. The form of optimal functions a(t) and b(t).

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3. Fig. 2. Change in the projections of the spacecraft kinetic moment during the turn.

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4. Fig. 3. Change of the components of the orientation quaternion L(t) during the reversal.

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5. Fig. 4. The type of functions p1(t), p2(t), p3(t) during the optimal reversal.

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6. Fig. 5. Change of the kinetic moment modulus under optimal control.

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