Schrodinger dynamics and Berry phase of undulatory locomotion

TL;DR

This paper demonstrates that mode-based linear models, incorporating physical symmetries, can accurately describe and classify undulatory locomotion across various organisms and robots using Schrödinger equations and Berry phases.

Contribution

It introduces a novel approach applying spectral mode representations and Schrödinger equations to characterize and differentiate locomotion behaviors in living and robotic systems.

Findings

Mode-based models accurately describe undulatory locomotion.

Eigenstates and Berry phases classify locomotion behaviors.

Approach generalizes to other physical and biological systems.

Abstract

Spectral mode representations play an essential role in various areas of physics, from quantum mechanics to fluid turbulence, but they are not yet extensively used to characterize and describe the behavioral dynamics of living systems. Here, we show that mode-based linear models inferred from experimental live-imaging data can provide an accurate low-dimensional description of undulatory locomotion in worms, centipedes, robots, and snakes. By incorporating physical symmetries and known biological constraints into the dynamical model, we find that the shape dynamics are generically governed by Schrodinger equations in mode space. The eigenstates of the effective biophysical Hamiltonians and their adiabatic variations enable the efficient classification and differentiation of locomotion behaviors in natural, simulated, and robotic organisms using Grassmann distances and Berry phases. While our analysis focuses on a widely studied class of biophysical locomotion phenomena, the underlying approach generalizes to other physical or living systems that permit a mode representation subject to geometric shape constraints.