State-feedback control of an internal rotor for propelling and steering a flexible fish-inspired underwater vehicle

This paper addresses the swimming dynamics and control of a flexible fish-inspired robot based on closed-loop control of an internal reaction wheel. Previous studies have shown that the dynamics of a rigid swimming robot are analogous to the canonical Chaplygin sleigh, due to the nonholonomic constraint imposed by the Kutta condition applied to the fishlike tail. The Chaplygin-sleigh dynamics are used here to design a propulsion and steering controller for a flexible swimming robot using state feedback. The desired average heading angle is achieved using a torque calculated from the instantaneous heading angle and rate. This feedback law stabilizes a limit cycle about the desired heading angle and produces forward swimming motion. Analysis of a global bifurcation in the dynamics under feedback control reveals the set of control gains that yield the desired limit cycle. Simulations illustrate planar swimming motion and preliminary experimental results are provided.