Curvature-based, time delayed feedback as a means for self-propelled swimming

The development of bio-inspired robotics has led to an increasing need to understand the strongly coupled fluid-structure and control problem presented by swimming. Usually, the mechanical forcing of muscles is modeled with an imposed distribution of bending moments along the swimmer's body. A simple way to exploit this idea is to define a central pattern forcing for this active driving, but this approach is not completely satisfactory because locomotion results from the interaction of the organism and its surroundings. Gazzola et al. (2015) have proposed that a curvature-based feedback with a time delay can trigger self-propulsion for a swimmer without necessitating such a pre-defined forcing. In the present work, we implement this feedback within a numerical model. We represent the swimmer as a thin elastic beam using a finite element representation which is coupled to an unsteady boundary element method for the resolution of the fluid domain. The model is first benchmarked on a flexible foil in forced leading edge heave. To recover previous findings, an imposed traveling bending moment wave is then used to drive the swimmer which yields peaks in the mean forward velocity when the driving frequency corresponds to the natural frequencies of the elastic structure. Delayed, curvature-based feedback is then applied to the swimmer and produces peaks in the velocity for delays that differ from the natural periods, associated to its deformations modes. Finally, a simplified model is shown to qualitatively describe the origin of the peaks observed in the feedback swimmer. (C) 2019 Elsevier Ltd. All rights reserved.