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Hydrodynamic interactions play a key role in the swimming behavior and powerconsumption of bio-inspired and bio-mimetic micro-swimmers, Cybernetic orartificial alike. As micro-robotic devices, bio-inspired micro-swimmers requirefast and reliable numerical models for robust control in order to carry outdemanding therapeutic tasks as envisaged for more than sixty years. The fastestknown numerical model, the resistive force theory (RFT), incorporates localviscous force coefficients with the local velocity of slender bodies in orderto find the resisting hydrodynamic forces, however, omitting the induced farfield altogether. In this scheme, the forces are calculated for a pure fluidresistance, however, at the expense of time-dependent hydrodynamic interactioneffects. As a result, the power requirement cannot be predicted accuratelyalthough the supply of necessary power is one of the biggest obstacles impedingthe micro-robotic efforts. In this study, an analysis strategy is proposed toimprove the RFT-based analysis, particularly for spermatozoa andspermatozoa-inspired micro-swimmers with elastic slender tails, in order topresent a practical solution to the problem. The required analytical correctionand the necessary correction coefficients are based on hydrodynamic impedanceanalysis via intensive computational fluid dynamics (CFD) models, i.e., thetime-dependent solution of 3-dimensional Navier-Stokes equations incorporatedwith deforming mesh and subject to conservation of mass. The CFD-based modelresults are then used to extract the correction coefficients with the help of acost function written based on the hydrodynamic power required to sustain thecontinuous swimming of selected shape and design. The performance of thecorrections embedded in the RFT model is finally validated against the CFDmodel by means of hydrodynamic power comparisons.

Hydrodynamic Impedance Correction for Reduced-Order Modeling and Real-Time Control of Spermatozoa-Like Soft Micro-Robots for Medicine