Continuum modeling and dynamics of earthworm-like peristaltic locomotion

Abstract

In this study, we present a continuous dynamics model for peristaltic rectilinear locomotion that accounts for three-dimensional deformation, inertia, friction, nonlinear constitutive profile, and strain waves. Using tensile tests and contact force measurements from earthworms, we derived the constitutive and anisotropic Coulomb's dry friction models. The developed dynamic model uniquely incorporates inertial effects and strain waves, the latter of which is a mathematical abstraction of the retrograde peristaltic wave mechanism and earthworm-like robotic gaits. We analyze locomotion dynamics under both force field and strain field, which reveal qualitatively similar peristaltic locomotion but different average velocities due to varying backward slippage. We further investigate the impact of inertia and strain wave parameters, finding that larger inertia under force fields increases backward sliding and reduces average velocity, while higher strain wave amplitudes under strain fields enhance velocity but also backward sliding. Anchoring and extension/contraction intervals in the strain wave also significantly affect the non-smooth stick-slip dynamics and the average velocity, and the results are consistent with previous studies on earthworm-like robot gaits. Overall, this research highlights the significance of the continuum dynamic model in analyzing the peristaltic locomotion of living earthworms. This model also holds promise for extending its use to the realm of robotics, providing valuable insights into the control and performance optimization of earthworm-like robots.