Control-oriented averaging of tail-actuated robotic fish dynamics

Motivated by the need for efficient control design, in this paper we consider the averaging of dynamics for a tail-actuated robotic fish, based on an experimentally validated dynamic model that incorporates rigid body dynamics and Lighthill´s large-amplitude elongated-body theory. We first show that classical averaging theory fails in this case because of the relatively large oscillatory input in the driving terms. On the other hand, while the first-order geometric averaging method for systems with highly oscillatory inputs is able to capture the original time-dependent dynamics, the resulting average model is overly complex for controller design. We propose a novel control-oriented, data-driven averaging approach for robotic fish dynamics, where a scaling function is introduced on top of the classical averaging method. We run extensive simulations for different combinations of tail-beat bias, amplitude, and frequency, and find that the scaling function is constant for the force equations and varies linearly with the tail-beat bias for the moment equation. The validity of the resulting average model has been confirmed in simulation results for open-loop dynamics with new sets of tail-beat parameters, and for closed-loop dynamics when proportional control of the tail-beat bias is used in target tracking.