Limit cycle dynamics of a Chaplygin sleigh - a surrogate model for fish like swimming*

The Chaplygin sleigh is a canonical problem in the area of nonholonomic systems. In recent work the constraint which governs the motion of the Chaplygin sleigh was shown to be similar to the Kutta condition which models the vortex shedding past the trailing edge of a Joukowski foil. Inspired by this similarity we investigate the dynamics of a Chaplygin sleigh subjected to viscous dissipation and a periodic input torque. The Chaplygin sleigh's velocities converge to a limit cycle under such actuation. Experiments on a Joukowski foil shaped robot confirm the existence of a similar limit cycle in its velocity space. We discuss analytical approximations of this limit cycle and show that this approximation is useful to control the motion and Chaplygin sleigh. The limit cycle dynamics then serve as a useful approximation for the swimming motion of a Joukowski foil.