Spacecraft spatial attitude control

M.V.Levsky

Research Institute of Space Systems, Khrunichev State research and production Space Center

Tikhonravov Street, 27, Jubileiniy, Moscow region, 141092, Russia

Development of economy modes and control algorithms of spacecraft attitude using jet micro-engines as executive devices is one of the most important problems of space engineering. The following aspects are considered in the paper: one of the modes of spacecraft (SC) motion control: the problem of synthesis of control algorithms for a spatial turn of arbitrary spacecraft without restrictions on mismatch angles, possessing rather high efficiency in comparison with known ways and rather easily realizable.

By spatial reorientation we mean shifting of spacecraft-fixed пXYZ axes from one known angular position into another known (usually given) angular position within finite time t_Л. In this case parameters of a turn (for example, components of a turn quaternion) are known beforehand, even prior to the beginning of maneuver; initial angular mismatches are arbitrary values (from several degrees to 180º). Thus angular attitude of the right-handed пXYZ coordinate system (as its initial пX_inY_inZ_in and final пX_fY_fZ_f positions) is determined relative to chosen reference basis I. In this paper the most widespread case is examined when inertial coordinate system пX_I Y_I Z_I (ICS) is considered as reference basis. The optimization problem of terminal control providing within fixed control time, t_Л, superposition of right-handed spacecraft-fixed пXYZ coordinate system on program basis whose position is given in inertial space, was investigated. A great number of papers cover various problem statements of optimal control over solid body reorientation. In particular, problems of optimal SC turn in terms of performance velocity or minimum power expenditures were considered before. Analytical solution was received by Pontryagin's principle of maximum for a case when admitted region of control moment is limited to a sphere, and SC itself turns around the vector of finite rotation. The optimal control was obtained using the method of combined synthesis on the basis of algorithm with predictive model, and functional of generalized work was minimized. Analytical designing by criterion of generalized work (бDGW) represents rather universal tool for solving optimal control problems. However, optimization by бDGW does not allow implementation of restrictions imposed on control variables. Besides, the controls synthesized by ADGW method, represent continuous (and even smooth) functions; they provide asymptotic approach to a required final state (angular position and velocity). Relay controls are optimal in terms of economy and efficiency. Essential бDGW's drawback is its unfitness for a case of arbitrary initial angular deviations (including unlimitedly high ones).

Using predictive models in controls synthesis raises quality of regulation and thereby they are widely applied now by many authors. But in such algorithms the final result depends basically on a kind of predictive model; the latter completely predetermines the type of a turn realized by received controls.

Optimization of SC reorientation by criterion of minimum fuel consumption represents certain difficulties both in mathematical and in computational aspect. Despite a large number of works covering this issue, the problem of deriving the optimal equations giving minimum fuel consumption, is still open. Present article considers obtaining some optimal program of spatial reorientation of arbitrary spacecraft.