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Many animals and robots move using undulatory motion of their bodies. When inclose proximity undulatory motion can lead to novel collective behaviors suchas gait synchronization, spatial reconfiguration, and clustering. Here we studythe role of contact interactions between model undulatory swimmers: three-linkrobots in experiment and multi-link robots in simulation. The undulatory gaitof each swimmer is generated through a time-dependent sinusoidal-like waveformwhich has a fixed phase offset, $\phi$. By varying the phase relationshipbetween neighboring swimmers we seek to study how contact forces and spatialconfigurations are governed by the phase difference between neighboringswimmers. We find that undulatory actuation in close proximity drivesneighboring swimmers into spatial equilibrium configurations that depend on theactuation phase difference. We propose a model for spatial equilibrium ofnearest neighbor undulatory swimmers which we call the gait compatibilitycondition, which is the set of spatial and gait configurations in which nocollisions occur. Robotic experiments with two, three, and four swimmersexhibit good agreement with the compatibility model. To probe the interactionpotential between undulatory swimmers we perturb the each longitudinally fromtheir equilibrium configurations and we measure their steady-statedisplacement. These studies reveal that undulatory swimmers in close proximityexhibit cohesive longitudinal interaction forces that drive the swimmers fromincompatible to compatible configurations. This system of undulatory swimmersprovides new insight into active-matter systems which move through bodyundulation. In addition to the importance of velocity and orientation coherencein active-matter swarms, we demonstrate that undulatory phase coherence is alsoimportant for generating stable, cohesive group configurations.

Lateral contact yields longitudinal cohesion in active undulatory systems