Development and experimental validation of a model for the membrane restoring torques in undulatory fin mechanisms

Bio-inspired undulatory fin propulsion holds considerable potential for enhancing the low-speed manuever-ability and hovering performance of unmanned underwater vehicles. Robotic fins typically comprise a number of serially arranged and individually actuated “fin rays”, interconnected by a membrane-like flexible surface, where appropriately timed ray oscillations lead to the propagation of an undulatory wave along the mechanism. In this context, we present an analytical model for the torques arising at the mechanism's revolute joints specifically from the elastic deformation of the membrane. The developed model, which considers the effect of various parameters, related to the fin's geometry, the membrane material properties, and the kinematics of the undulatory wave, is validated through comprehensive experimental studies with a two-ray testbed operating in air.