Walking and running on yielding and fluidizing ground

Abstract

We study the detailed locomotor mechanics of a small, lightweight robot (DynaRoACH, 10 cm, 25 g) which can move on a granular substrate of closely packed 3 mm diameter glass particles at speeds up to 50 cm/s (5 body length/s), approaching the performance of small, highperforming, desert-dwelling lizards. To reveal how the robot achieves this high performance, we used high speed imaging to capture kinematics, and developed a numerical multi-body simulation of the robot coupled to an experimentally validated discrete element method (DEM) simulation of the granular media. Average forward speeds measured in both experiment and simulation agreed well, and increased non-linearly with stride frequency, reflecting a change in the mode of propulsion. At low frequencies, the robot used a quasi-static "rotary walking" mode, in which the granular material yielded as the legs penetrated and then solidified once vertical force balance was achieved. At high frequencies, duty factor decreased below 0.5 and aerial phases occurred. The propulsion mechanism was qualitatively different: the robot ran rapidly by utilizing the speed-dependent fluid-like inertial response of the material. We also used our simulation tool to vary substrate parameters that were inconvenient to vary in experiment (e.g., granular particle friction) to test performance and reveal limits of stability of the robot. Using small robots as physical models, our study reveals a mechanism by which small animals can achieve high performance on granular substrates, which in return advances the design and control of small robots in deformable terrains.

The dynamics of legged locomotion in heterogeneous terrain: universality in scattering and sensitivity to initial conditions

“…In our previous results, we noticed that the robot's trajectories were sensitive to initial conditions in both experiment and our multi-particle DEM simulation [21]. Fig.…”

Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides)

“…Analogous to hydrodynamic forces in fluids (Vogel, 1996), for an intruder moving rapidly in granular media, the particles initially at rest in front of the intruder are accelerated by, and thus exert reaction forces on, the intruder. Hydrodynamic-like forces at ~1ms -1 can play an important role both in impact forces on free-falling intruders (Katsuragi and Durian, 2007;Goldman and Umbanhowar, 2008) and in legged locomotion of small lightweight robots (Qian et al, 2012). We note that the foot rotation hypothesis should hold regardless, because hydrodynamic-like forces are also proportional to projected area (Katsuragi and Durian, 2007).…”

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

“…However, during fast locomotion, RFT is an insufficient descriptor of locomotion dynamics in granular media. For example, the performance of the DynaRoACH's high speed gaits [256] deviated from the rotary walking model, which, similar to RFT, assumes of quasistatic interactions. This deviation implies that hydrodynamic-like granular inertial effects contributed significantly to the reaction force, making quasistatic continuum equations like RFT ineffective.…”

“…(d) Time sequeneces of the two locomotion modes observed for DynaRoACH moving on 3 mm glass particles. Adapted from[256].…”