MODELING THE DYNAMICS OF SPRING-DRIVEN OSCILLATING-FOIL PROPULSION

In this paper we present a model for oscillating-foil propulsion in wh ich springs are used to transmit forces from the actuators to the foil . The expressions for hydrodynamic force and moment on the foil come f rom classical, linear, unsteady aerodynamics, and these are coupled to linearized rigid-body mechanics to obtain the complete model for swim ming. The model is presented as a low-order set of ordinary differenti al equations, which makes it suitable for the application of technique s from systems and control theory. The springs serve to reduce energy costs, and rye derive explicit expressions for spring constants which are optimal in this sense, However, the use of springs can potentially lead to unstable dynamics. Therefore, we also derive a set of necessa ry and sufficient conditions for stability. A detailed example is pres ented in which energy costs for one actuator are reduced by 33%.