Analytical modeling and experimental studies of robotic fish turning

Turning is one of the most important maneuvers for biological and robotic fish. In our group's prior work, an analytical framework was proposed for modeling the steady turning of fish, given asymmetric, periodic body/tail movement or deformation. However, the approach was not illustrated with simulation or validated with experiments. The contributions of the current paper are three fold. First, an extension to the modeling framework is made with a more rigorous formulation of the force balance equation. Second, we have worked out two examples explicitly, one with an oscillating, rigid tail, and the other with a flexible tail having a uniform curvature, and compared their turning behaviors through numerical results. Third, for model validation purposes, a robotic fish prototype has been developed, with the tail shaft controlled precisely by a servo motor. For a rigid tail, experimental results have confirmed the model prediction that, for the tested range, the steady-state turning radius and turning period decrease with an increasing bias in the tail motion, and that the turning period drops with an increasing tail beat frequency. We have also found that, with a flexible fin attached to the tail shaft, the robot can achieve faster turning with a smaller radius than the case of a rigid fin, and modeling within the same framework is underway to understand this phenomenon.