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

Abstract

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. [1] 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.

A spinal organ of proprioception for integrated motor action feedback

“…The central proprioceptor organ provides rapid inhibitory feedback that scales with body bending, which, in turn, could counteract the output of the actuator with appropriate timing to terminate motor neuron drive. Recent modeling studies have shown that similar curvature-based proprioceptive feedback mechanisms that constrain body amplitudes are necessary to recapitulate fast and efficient locomotion (Gazzola et al, 2014(Gazzola et al, , 2015Gross et al, 2019), but until now, the biological basis for this mechanism has been unknown.…”

Optimum Curvature Characteristics of Body/Caudal Fin Locomotion

“…From the biological perspective, the curvature is controlled mostly by internal muscular activation. Specifically, fish can receive the stretch receptors that depend on body curvature to the central nervous system and then drive the calcium dynamics to affect the muscle activity, which can further modulate the swimming behavior [12,13]. Many in vivo experiments and electromyogram analyses have been conducted to discover the neuro-musculo-mechanical model, and much progress on the model has been made [14][15][16][17][18].…”