ISSN 0005-1179, Automation and Remote Control, 2018, Vol. 79, No. 3, pp. 524–534.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
V.M. Glumov, I.N. Krutova, V.M. Sukhanov, 2016, published in Problemy Upravleniya, 2016, No. 1, pp. 82–89.
Some Features of Powered Gyrostabilization
of a Large Space Structure Assembled in Orbit
V. M. Glumov
, and V. M. Sukhanov
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia
Received June 10, 2015
Abstract—This paper presents the single-axis angular motion equations of a large space struc-
ture assembled in orbit from separate elastic construction elements. We introduce a method to
calculate the parameters of discretely varying dynamical properties of an assembled structure
whose model has variable coeﬃcients and inherent attributes of an elastic multi-frequency vi-
brating system. In addition, we suggest a parametrically tuneable algorithm for powered gyro
control of such objects that guarantees desired dynamics at all steps of robotized assembly.
Simulation results demonstrate the eﬃciency of the suggested algorithm.
Keywords: large space structure, orbital assembly, mathematical model, powered gyro control,
This paper considers some gyrostabilization problems for the angular position of large space
structures (LSSs) in the process of their element-wise robotized assembly in orbit . The speciﬁcs
of such objects (e.g., space radio telescopes and solar energy retransmitters [2, 3]) consist in a
discretely varying structure and an essential elasticity of the whole structure assembled. Therefore,
as a control object an LSS represents a dynamical system with time-varying coeﬃcients and a
large time-varying number of degrees of freedom that has inherent attributes of an elastic multi-
frequency vibrating system. In the earlier paper , this system was called a discretely developing
construction (DDC). As a mechanical system, a DDC can be treated as a certain sequence of partial
mechanical structures that arise in the course of assembly.
For deﬁniteness, we choose the model of an “umbrella” LSS suggested in  as the object of
research. This model is a good description of regular structures like large space mirrors or radio
telescopes, see [2, 3].
At each step of assembly, the DDC represents a set of n+ 1 bodies (Fig. 1), one of which (shaded
in Fig. 1) is a central carrying body of mass m
and inertia moment I
. The other bodies with
the parameters m
, i = 1,n, n ∈ [1,N], where N gives their total number, are carried by
the central body. They represent rod-type construction elements (i.e., one-dimensional bodies of
reduced to the end of a weightless elastic rod of length l
) that are mounted on the carrying
body at given points o
) in a deﬁnite order. The elasticity of the rod elements induces
small displacements q
of the end masses from an equilibrium state. The structural damping of
elastic vibrations is neglected.
Without loss of generality, assume that the translational motion of a rod element mounted on
the carrying body is directed towards the radius vector that connects a corresponding mounting
to the pole o.