Localization and delocalization of a limbless robot in a 2D random lattice

Locomotion in disordered environments emerges from the interplay of body mechanics, terrain geometry, and control. Extending our prior one-dimensional study [Pierce and Wang et al., 2025], we examine a 10-joint limbless robot (BL=0.4m) in experiments and multi-body physics simulations traversing a 2D triangular lattice consisting of "boulders" (spherical caps) with controlled spacing, height, and disorder. Intrinsic drag anisotropy (DA), introduced by attaching passive wheels, enables net forward propulsion without boulder interaction. For increasing lattice disorder (implemented by randomly perturbing the base triangular lattice), we observe a transition between lattice-traversal and localized dynamical states in the robot; localization occurs when the robot can no longer generate net forward motion despite continuous actuation. At low disorder, propulsion arises when the body wavelength matches the terrain spacing, forming resonant coupling that produces extrinsic DA. At high disorder, the robot's intrinsic DA is essential for transport. To identify minimal strategies that delocalize the robot, we introduce stochastic run-and-tumble behaviors. These dynamics partially delocalize the robot, though the effect diminishes under strong disorder. We posit that feedback controlled active behaviors, such as reversals, are required to delocalize the robot at strong disorder, establishing a hierarchy of delocalization strategies.