Attitude Control of a Rigid Body by Means of Internal Movable Masses

This chapter addresses the control of the motion of systems with movable internal point masses in the absence of external forces. In this case, it is impossible to control the motion of the center of mass, however, the orientation of the housing can be controlled. This possibility is of interest for the attitude control of spacecraft and other vehicles, as well as for the control of the orientation of a mobile capsule robot when performing rapid turns, in which case the influence of the external forces can be neglected as compared with the internal forces caused by the motion of the internal masses. The modes of the attitude control by means of one or several internal masses are constructed. The objective of the control is to provide a desired orientation for the housing. Three sections of this chapter are devoted to the plane motion of the system with one internal mass. In the plane motions, the housing performs parallel plane motions in the inertial space, while the internal point mass moves along a curve (not given in advance) in a plane that is parallel to the plane of the motion of the housing. Optimal control problems in which the housing is required to be rotated by a given angle in a minimal time are solved. It is assumed that the system is at rest in the initial and terminal states and that the initial position of the internal mass relative to the housing is given. The terminal position of the internal mass in the reference frame attached to the housing may be free, fixed partly (e.g., one coordinate is fixed, while the other coordinate is free) or fixed completely. The components of the relative velocity of the internal mass in the reference frame attached to the housing are used as the control variables. The absolute value of this velocity is subjected to a constraint. Two remaining sections deal with a spatial (triaxial) reorientation of the housing by using one internal point mass or several internal point masses. It is shown that using several (more than three) internal point masses allows substantially simplifying the structure of the control system.