Optimal Undulatory Swimming with Constrained Deformation and Actuation Intervals

TL;DR

This study uses reinforcement learning to identify optimal undulatory swimming patterns in microswimmers constrained by local actuation and stiffness, revealing how internal constraints influence efficient beating behaviors.

Contribution

It introduces a novel approach combining reinforcement learning with constrained bead-bend-spring models to discover optimal undulatory swimming patterns under local actuation constraints.

Findings

Optimal beating patterns depend on action intervals and intrinsic stiffness.

Bang-bang torque solutions with specific periodicity and phase shifts are optimal.

The results provide insights into biological microswimmer efficiency and artificial actuation strategies.

Abstract

In nature, many unicellular organisms are able to swim with the help of beating filaments, where local energy input leads to cooperative undulatory beating motion. Here, we investigate by employing reinforcement learning how undulatory microswimmers modeled as a discretized bead-bend-spring filament actuated by torques which are constrained locally. We show that the competition between actively applied torques and intrinsic bending stiffness leads to various optimal beating patterns characterized by distinct frequencies, amplitudes, and wavelengths. Interestingly, the optimum solutions depend on the action interval, i.e.\ the time scale how fast the microswimmer can \rev{change the applied torques} based on its internal state. We show that optimized stiffness- and action-interval-dependent beating is realized by bang-bang solutions of the applied torques with distinct optimum time-periodicity and phase shift between consecutive joints, which we analyze in detail by a systematic study of possible bang-bang wave solution patterns of applied torques. Our work not only sheds light on how efficient beating patterns of biological microswimmers can emerge based on internal and local constraints, but also offers actuation policies for potential artificial elastic microswimmers.