On special cases of a problem of an optimal control of angular movement of symmetric spacecraft stabilized by rotation

Аuthors

Sirotin A. N.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: asirotin2@mail.ru

Abstract

Stabilization by rotation and stabilization of a spacecraft relative to the three axes are the main methods employed to maintain the exact solid body orientation. The idea of rotation stabilization is based on the application of a gyroscopic effect. The advantage of this method, compared to the other approaches, consists in simplicity and the lack of a prolonged active rotation period to maintain orientation in a certain direction. Rotational stabilization was being employed for a large number of foreign and Soviet/Russian spacecraft. Application of rotation stabilization for passive control is relevant for spacecraft with limited resources. However, the shortcomings of the passive stabilization method are also well known and are associated mainly with the problem of the exact reorientation of space antennas and optics. Thus, frequently used maneuvers for angular motion lead to the need to resort to solving problems of controlling the exact reorientation in three-dimensional space.

The article studies the problem of angular motion optimal control of a rigid body by stabilized rotation. The efficiency criterion of is a minimum of energy costs. Compared to the general problem of reorientation and rotation control, the problem of bodies with stabilized rotation from the mathematical viewpoint is somewhat simpler. It is explained by reduction of dimensionality and complexity of the corresponding nonlinear equations of the system. Nevertheless, the problem of controlling joint reorientation and rotation remains complex and nonlinear. This, in turn, does not allow obtaining the required analytical result at the given time. Therefore, the purpose of this article is to obtain a characterization of extremal trajectories. There is a possibility to study in detail the problem of zero stabilization by rotation, when the projection of the angular velocity on one of the axes is identically zero.

Keywords:

optimal control, reorientation, symmetric solid body, energy consumption, maximum principle

References

1. Hall C.D., Rand R.H. Spinup dynamic of axial dual-spin spacecraft, Journal of Guidance, Control and Dynamics, 1994, vol. 17, no. 1, pp. 30-37.

2. Meehan P.A., Asokanthan S.F. Control of chaotic motion in a dual – spin spacecraft with nutational damping, Journal of Guidance, Control and Dynamics, 2002, vol. 25, no. 2, pp. 209-214.

3. Bao G.W., Pascal M. Stability of spinning liquid-filled spacecraft, Applied Mechanics, 1997, vol. 67, pp. 407-421.

4. Tsiotras P., Longuski J.M. Spin-axis stabilization of symmetric spacecraft with two control torques, Systems and Control Letters, 1994, vol. 23, pp. 395-402.

5. Biggs J.D., Horri N. Optimal geometric motion planning for a spin-stabilized spacecraft, Systems and Control Letters, 2012, vol. 61, pp. 609-619.

6. Sirotin A.N. Vestnik Moskovskogo aviatsionnogo instituta, 2010, vol. 17, no. 4, pp. 58-63.

7. Akulenko L.D., Nikolaev N.V. Kosmicheskie issledovaniya, 1991, vol. 29, no. 6. pp. 849 – 857.

8. Levskij M.V. Vestnik Moskovskogo aviatsionnogo instituta, 2008, vol. 15, no. 3, pp. 129-140.

9. Beschastnyi I.Yu. Matematicheskii sbornik, 2014, vol. 205, no. 2, pp. 2-38.

Download