The design and control of underwater robots has to contend with the coupled robot-hydrodynamic interactions. A key aspect of this coupled dynamics is the interaction of the robot with the fluid via the vorticity that is created by the robot’s motion. In this paper we develop a simplified and very low dimensional model of this interaction. This is done recognizing that the vortex shedding is a nonholonomic constraint. We apply the harmonic balance approach to analyze and compare the limit cycle in the dynamics of the fish-shaped body propelled by a periodic input with that of a Chaplygin sleigh, a well known nonholonomic system. The dynamics on the limit cycles lead to a very low dimensional model of the swimming of the fish-shaped body that could be very useful from the perspective of controlling a swimming robot.

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