Averaging Tail-Actuated Robotic Fish Dynamics Through Force and Moment Scaling

Averaging of robotic fish dynamics is of interest for the purposes of path planning and controller design due to the rhythmic movement of the robot. For a faithful dynamic model of robotic fish, however, classical averaging or geometric averaging typically cannot produce an average model that is accurate and in the meantime amenable to analysis or control design. In this paper, a novel averaging approach is proposed for tail-actuated robotic fish dynamics, in which the tail-generated hydrodynamic force is modeled with the Lighthill´s large-amplitude elongated-body theory. The approach consists of scaling the force and moment terms and, then, conducting classical averaging. Numerical investigation reveals that the scaling function for the force term is a constant independent of tail-beat patterns, while the scaling function for the moment term depends linearly on the tail-beat bias. Extensive simulation and experimental results, comparing the predictions from the original and average models, are presented to support the effectiveness of the averaging approach. Existence and local stability of the equilibria for the average model are further analyzed. These equilibria are subsequently used to obtain an analytical solution for steady turning parameters, such as turning period and turning radius, without running simulation of the original or average dynamic models.