The new algorithm of quasi-optimal reorientation of a spacecraft

Ya. G. Sapunkov ; A. V. Molodenkov

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 23 (2023) no. 1, pp. 95-112

Résumé

The classical problem of optimal control of the attitude maneuver of a spacecraft as a rigid body of arbitrary dynamic configuration under arbitrary boundary conditions for the angular position and angular velocity of a spacecraft without restriction on the control vector function and with a fixed transition time is considered. As a criterion of optimality, the functional of the energy spent on the rotation of a spacecraft is used. Within the bounds of the Poinsot concept describing arbitrary angular motion of a rigid body in terms of generalized conical motion, a modification of the problem of optimal control of the angular motion of a spacecraft is carried out and its trajectory is given in this class of motions. At the same time, the generality of the original problem is practically not violated, since the known exact solutions to the classical problem of optimal angular motion of a dynamically symmetric spacecraft in cases of plane rotation or regular precession and similar solutions of the modified problem completely coincide; in other cases, in numerical calculations of the classical and modified problems, the discrepancy between the values of the optimization functional is no more than a few percent, including spacecraft rotations at large angles. Therefore, the proposed solution of the modified problem can be used as quasi-optimal with respect to the classical problem. Explicit expressions for the quaternion of the orientation and the vector of angular velocity of a spacecraft are given, a formula for the vector of the control moment of a spacecraft is obtained based on the solution of the inverse problem of the dynamics of a rigid body. The quasi-optimal algorithm for optimal rotation of a spacecraft is given. Numerical examples showing the proximity of solutions to the classical and modified problems of optimal reorientation of a spacecraft are given.