Elastic-instability-enabled locomotion

Abstract

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement--via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments--both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales.

Keywords: buckling; elastic instability; locomotion.

Fig. 1.

Schematic representation of the choices of variables available to engineer locomotion. Geometry and material choices make up a system that uses a power source and, on interaction with the environment, causes symmetry breaking, leading to a net directional movement. Buckling of a thin circular sheet is one of the simplest mechanisms of symmetry breaking of an axisymmetric system.

Fig. 2.

Locomotion of buckling-sheet actuator with scaling law in terrestrial environment. (A) Photos of crawling motion of the buckling-sheet actuator with d = 20 cm on a rough surface. (B) Displacement vs. time plot for crawling of the buckling-sheet actuator with different d values for ω = 0.5 Hz. (C) v_c/(ω d) vs. h plot to show the scaling law for crawling with d = 20 cm. The coefficient (slope of linear fit) is ∼0.6 (R² ∼ 0.81). All measurements were performed with pneumatic input for buckling of the sheet and vacuum for unbuckling of the sheet. θ_c in A is the contact angle between the “foot” of the conimal and the surface.

Fig. 3.

Locomotion of buckling-sheet actuator in aquatic environment. For swimming motion, the actuator with different diameters (d) was actuated with a constant buckling frequency (ω_B) and varying unbuckling frequency (ω_U). (A) Photos of buckling-sheet actuator with d = 20 cm swimming on the surface of water. The actuator moves only when the buckling frequency (ω_B) is larger than the unbuckling frequency (ω_U). (B) Displacement vs. time plot for swimming of the buckling-sheet actuator with different d values for ω_B ∼ 0.83 Hz and ω_R ∼ 0.36 Hz. (C) The plot of the scaling law for swimming, v_S/[(ω_B – ω_U) d)] vs. h/d with d = 20 cm. The coefficient (slope of linear fit) is ∼0.5 (R² ∼ 0.86).