Independent caudal fin actuation enables high energy extraction and control in two-dimensional fish-like group swimming

We study through numerical simulation the optimal hydrodynamic interactions and basic vorticity control mechanisms for two fish-like bodies swimming in tandem. We show that for a fish swimming in the wake of an upstream fish, using independent pitch control of its caudal fin, in addition to optimized body motion, results in reduction of the energy needed for self-propulsion by more than 50 %, providing a quasi-propulsive efficiency of 90%, up from 60 % without independent caudal fin control. Such high efficiency is found over a narrow parametric range and is possible only when the caudal fin is allowed to pitch independently from the motion of the main body. We identify the vorticity control mechanisms employed by the body and tail to achieve this remarkable performance through thrust augmentation and destructive interference with the upstream fish-generated vortices. A high sensitivity of the propulsive performance to small variations in caudal fin parameters is found, underlying the importance of accurate flow sensing and feedback control. We further demonstrate that using lateral line-like flow measurements to drive an unscented Kalman filter, the near-field vortices can be localized within 1 % of the body length, and be used with a phase-lock controller to drive the body and tail undulation of a self-propelled fish, moving within the wake of an upstream fish, to stably reach the optimal gait and fully achieve maximum energy extraction.