Collective Synchronization of Undulatory Movement through Contact

Abstract

Many biological systems synchronize their movement through physical interactions. By far, the most well-studied examples concern physical interactions through a fluid: Beating cilia, swimming sperm and worms, and flapping wings all display synchronization behavior through fluid mechanical interactions. However, as the density of a collective increases, individuals may also interact with each other through physical contact. In the field of "active matter"systems, it is well known that inelastic contact between individuals can produce long-range correlations in position, orientation, and velocity. In this work, we demonstrate that contact interactions between undulating robots yield novel phase dynamics such as synchronized motions. We consider undulatory systems in which rhythmic motion emerges from time-independent oscillators that sense and respond to an undulatory bending angle and speed. In pair experiments, we demonstrate that robot joints will synchronize to in-phase and antiphase oscillations through collisions, and a phase-oscillator model describes the stability of these modes. To understand how contact interactions influence the phase dynamics of larger groups, we perform simulations and experiments of simple three-link undulatory robots that interact only through contact. Collectives synchronize their movements through contact as predicted by the theory, and when the robots can adjust their position in response to contact, we no longer observe antiphase synchronization. Lastly, we demonstrate that synchronization dramatically reduces the interaction forces within confined groups of undulatory robots, indicating significant energetic and safety benefits from group synchronization. The theory and experiments in this study illustrate how contact interactions in undulatory active matter can lead to novel collective motion and synchronization.