Lateral contact yields longitudinal cohesion in active undulatory systems

TL;DR

This study investigates how contact interactions and phase differences between undulatory swimmers influence their spatial arrangements and cohesion, revealing a model for stable configurations and the importance of phase coherence in active matter systems.

Contribution

The paper introduces the gait compatibility condition model for undulatory swimmers, linking phase differences to stable spatial configurations and cohesion, supported by experiments and simulations.

Findings

Contact forces promote stable spatial configurations based on phase differences.

The gait compatibility condition predicts collision-free arrangements.

Undulatory phase coherence enhances group stability and cohesion.

Abstract

Many animals and robots move using undulatory motion of their bodies. When in close proximity undulatory motion can lead to novel collective behaviors such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multi-link robots in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, $\phi$. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and spatial configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into spatial equilibrium configurations that depend on the actuation phase difference. We propose a model for spatial equilibrium of nearest neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of spatial and gait configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To probe the interaction potential between undulatory swimmers we perturb the each longitudinally from their equilibrium configurations and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit cohesive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.