Rectilinear Periodic Motions of Systems with Internal Bodies

In this chapter, we consider rectilinear motions of mobile systems that move in resistive media without external propelling devices (legs, wheels, caterpillars, fins, screw propellers, etc.) due to the motion of internal bodies. Such systems consist of a rigid housing and internal bodies that can move relative to the housing under the action of drives. The drives implement the interaction of the internal bodies with the housing of the locomotion system. The housing interacts also with the environment, whereas the internal bodies do not interact with the environment. A force applied by the drive to an internal body causes a reaction force applied to the housing, as a result of which the velocity of the housing relative to the environment changes. The change in the velocity of the housing leads to a change in the resistance (friction) force applied by the environment to the housing. The forces generated by the drives are internal forces for the mechanical system under consideration (the housing plus the internal bodies), while the environment resistance force is an external force. Thus, by controlling the motion of the internal bodies due to internal forces one can control the external force applied to the locomotion system and thereby the motion of the system as a whole. Mobile robots that move due to the motion of internal bodies are frequently called capsule robots (capsubots). The capsule robots have a number of advantages over mobile systems of other types. The capsule robots are simple in design, do not need complex mechanisms to transmit the motion from the drives to the propelling devices, are easy to miniaturize, and their housings can be made hermetic and geometrically smooth, without protruding pieces. The last circumstance enables the capsule robots to be used in vulnerable environments, in particular, in medicine for diagnosis inspections inside a human body or for precise delivery of a drug to an affected area. Capsule robots can be used also for motion inside thin tubes, for example, for their technical inspection, or in narrow slots. A number of control and optimization problems for capsule robots are solved.