Buckling Configuration Design of Two Nested Elastic Rings Under Gravity for Rolling Soft Robot

The design of the buckling configuration for a rolling soft robot has a significant effect on its rolling performance, but a thorough analysis remains lacking for many soft robot buckling configurations because of the difficulty of analyzing the buckling problem. This work comprehensively analyzes the static buckling morphology of two nested elastic rings under gravity based on a theoretical model using the minimum potential energy principle. Two nested rings present a tank-track-like buckling morphology under gravity, which depends on the length ratio, the bending stiffness ratio, and the gravity ratio of the inner ring to the outer ring. Increases in these three ratios lead to a lower tank-track-like buckling structure with an increased ground contact length and a reduced gravity moment on the slope. The tank-track-like buckling structures predicted using the theory agree well with Finite Element Method (FEM) simulations and experimental results. This work provides design guidance on achieving the maximum slope stability and the required robot configuration by tuning the geometrical and material parameters of rolling soft robots.