Abstract
Locomotion of a mechanical system consisting of two rigid bodies, a main body and a tail, is considered. The system moves in a resistive fluid and is controlled by angular oscillations of the tail relative to the main body. The resistance force acting upon each body is assumed to be a quadratic function of its velocity. Under certain assumptions, a nonlinear equation is derived that describes the progressive motion of the system as a whole.
The average velocity of this motion depending on the angular oscillations of the tail is estimated. The optimal control problem for the time history of these oscillations that maximizes the average velocity of the progressive motion is formulated and solved. Explicit expressions for the maximum average velocity and the corresponding optimal angular motion of the tail are obtained.
The results correlate well with observations of swimming and can be applied to swimming robotic systems.
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This work was supported by the Russian Foundation for Basic Research (Project 08-01-00411).
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Chernousko, F.L. Optimal Motion of a Two-Body System in a Resistive Medium. J Optim Theory Appl 147, 278–297 (2010). https://doi.org/10.1007/s10957-010-9722-1
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DOI: https://doi.org/10.1007/s10957-010-9722-1