The role of symmetry and dissipation in biolocomotion

Abstract

In this paper we illustrate the potential role which relative limit cycles may play in biolocomotion. We do this by describing, in great detail, an elementary example of reduction of a lightly dissipative system modeling crawling-type locomotion in 3D. The symmetry group SE(2) is the set of rigid transformations of the horizontal (ground) plane. Given a time-periodic perturbation, the system will admit a relative limit cycle whereupon each period is related to the previous by a fixed translation and rotation along the ground. This toy model identifies how symmetry reduction and dissipation can conspire to create robust behavior in crawling, and possibly walking, locomotion.

41 pages, 8 figures; final version as published

References in corpus (4)

• Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
• Geometric visualization of self-propulsion in a complex medium
• Crawling scallop: Friction-based locomotion with one degree of freedom
• On the Damping-Induced Self-Recovery Phenomenon in Mechanical Systems with Several Unactuated Cyclic Variables

Cited by in corpus (7)

• A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems
• Global linearization and fiber bundle structure of invariant manifolds
• Rate-independent soft crawlers
• Gait modeling and optimization for the perturbed Stokes regime
• Limit cycles for dynamic crawling locomotors with periodic prescribed shape
• A Hybrid Dynamical Extension of Averaging
• Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction