Disorder-Induced Transition from Ballistic Motion to Localization in a Limbless Undulating Robot

Limbless undulators like snakes and nematodes move in environments which mix homogeneous substrates with rigid obstacles. Inspired by our previous discoveries of“mechanical diffraction” of snakes and robots [Rieser et al, 2019] in regular 1D arrays perpendicular to the direction of travel, we test if diffractive effects persist when a robot is forced to move in a 1D array along its travel direction. Specifically, we simulated a 13-joint limbless robot (wavelength 0.46m) locomoting through a regular 1D lattice (separation distance = 0.23m) of sphere-shaped boulders, which model spatially varied drag anisotropy, in a channel that constrains its motion to approximately one dimension. To model aperiodicity, a perturbing lattice is introduced consisting of boulders at a height Δ and with a separation distance of 1/β times the base lattice separation distance. We observe a drop of the mean-square displacement slope to 0 as Δ increases for all β except β = 0.5, indicating a transition to localization. This transition happens at lower Δ for irrational values of β, like the Aubry-André model that describes metal-insulator transitions in crystals. The mechanism of localization in the robot consists of either jamming or being unable to produce thrust to move forward. Robophysical experiments reveal similar effects. This approach to systematically studying locomotion in simple lattices suggests that solid state physics principles can be applied to robot locomotion in natural disordered environments.