Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler

TL;DR

This paper models the locomotion of a bio-inspired two-segment crawler using concepts from elasto-plasticity, identifying stasis domains and slip surfaces that determine when the crawler moves or stays still, with explicit solutions for certain cases.

Contribution

It introduces a novel framework linking elastic tensions to plastic flow rules to analyze crawler locomotion, providing explicit solutions and insights into actuation strategies.

Findings

Support sliding occurs only on slip surfaces.

Certain actuation strategies can induce net displacement.

The model reveals conditions for effective locomotion based on friction parameters.

Abstract

We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.