Optimal control of the motion of a multilink system in a resistive medium

The optimal control of the motion of a system consisting of a main body and one or two links joined to it by cylindrical joints in a resistive medium is investigated. The resistance force of the medium acting on the moving body is assumed to depend on their velocity. The control is accomplished through high-frequency angular oscillations of the links. The equations of motion are analysed, and the mean velocity of translational motion of the system is estimated under certain assumptions. Optimal control problems are formulated and solved, and the laws of control of the oscillations of the links for which the maximum mean velocity of motion is obtained are found as a result. The data obtained are in qualitative agreement with observations of the swimming of fish and animals. The results of this study can be used in developing mobile robots that move in a liquid.