Sensitive dependence of the motion of a legged robot on granular media

TL;DR

This study investigates how a legged robot's speed on granular media depends on control parameters and media properties, revealing a transition from walking to swimming modes and emphasizing the complex physics involved.

Contribution

It provides empirical insights and a kinematic model explaining the robot's locomotion modes on granular media, highlighting the sensitivity to packing fraction and limb frequency.

Findings

Robot speed on granular media is much lower than on hard ground with standard control.

Adjusting control parameters improves robot speed significantly.

A transition from rotary walking to swimming occurs with changes in packing fraction and limb frequency.

Abstract

Legged locomotion on flowing ground ({\em e.g.} granular media) is unlike locomotion on hard ground because feet experience both solid- and fluid-like forces during surface penetration. Recent bio-inspired legged robots display speed relative to body size on hard ground comparable to high performing organisms like cockroaches but suffer significant performance loss on flowing materials like sand. In laboratory experiments we study the performance (speed) of a small (2.3 kg) six-legged robot, SandBot, as it runs on a bed of granular media (1 mm poppy seeds). For an alternating tripod gait on the granular bed, standard gait control parameters achieve speeds at best two orders of magnitude smaller than the 2 body lengths/s ($\approx 60$ cm/s) for motion on hard ground. However, empirical adjustment of these control parameters away from the hard ground settings, restores good performance, yielding top speeds of 30 cm/s. Robot speed depends sensitively on the packing fraction $\phi$ and the limb frequency $\omega$, and a dramatic transition from rotary walking to slow swimming occurs when $\phi$ becomes small enough and/or $\omega$ large enough. We propose a kinematic model of the rotary walking mode based on generic features of penetration and slip of a curved limb in granular media. The model captures the dependence of robot speed on limb frequency and the transition between walking and swimming modes but highlights the need for a deeper understanding of the physics of granular media.