Aubry-André Transition for an Active Undulator

Abstract: The transport of deformable self-propelling objects like bacteria, worms, snakes, and robots through heterogeneous environments is poorly understood. In this paper, we use experiment, simulation, and theory to study a snake-like robot as it undulates without sensory feedback through a narrow channel containing a linear array of boulder-like hemispherical obstacles. The profile of the boulder landscape approximates a one-dimensional bichromatic potential introduced by Aubry and Andr\'e (AA) to study the propagation and localization of waves. When the boulder landscape is strictly periodic, the robot can pass completely through the channel. But if the landscape is sufficiently aperiodic, the robot can become trapped and fail to exit the channel. The metrics we use to quantify this change agree well with earlier experimental and theoretical work on a localization transition that occurs when quantum waves interact with the AA potential. A theoretical treatment of the robot's motion using resistive force theory modified to include spatially varying drag forces reproduces the behavior we observe.