# Efficient sliding locomotion with isotropic friction

## TL;DR

This paper investigates the efficiency of sliding locomotion in isotropic friction environments, proposing a numerical method and identifying optimal motions that leverage static friction, with implications for snake robots.

## Contribution

It introduces a regularized model for sliding locomotion with static friction and develops a numerical method to find efficient motions under isotropic Coulomb friction.

## Key findings

- Simple undulatory motions yield little net movement in isotropic friction.
- Three local efficiency optima are identified for time-harmonic motions.
- Certain smooth motions inspired by concertina locomotion achieve high efficiency.

## Abstract

Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction.