Two- and three-dimensional motions of a body controlled by an internal movable mass

The prescribed movement of a rigid body can be achieved by means of auxiliary internal masses performing special motions relative to the body. This principle of movement is used in mobile robots (capsule robots, vibro-robots) and is also applicable to the attitude control of spacecraft. Whereas one-dimensional motions of bodies controlled by internal movable masses are well-studied, two- and three-dimensional motions of such systems are not investigated thoroughly. In the paper, these motions are considered in the absence of external forces. Two-dimensional time-optimal motions of a body controlled by an internal mass are obtained for the case where the internal mass is small compared to the mass of the body. Based on this solution, suboptimal controls are presented for the general case. An approach to three-dimensional motions of such systems is presented which is based on three two-dimensional optimal rotations.

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