General scaling relations for locomotion in granular media

Robotic feet modeled after ungulates improve locomotion on soft wet grounds

Locomotion on soft yielding grounds is more complicated and energetically demanding than on hard ground. Wet soft ground (such as mud or snow) is a particularly difficult substance because it dissipates energy when stepping and resists extrusion of the foot. Sinkage in mud forces walkers to make higher steps, thus, to spend more energy. Yet wet yielding terrains are part of the habitat of numerous even-toed ungulates (large mammals with split hooves). We hypothesized that split hooves provide an advantage on wet grounds and investigated the behavior of moose legs on a test rig. We found that split hooves of a moose reduce suction force at extrusion but could not find conclusive evidence that the hoof reduces sinkage. We then continued by designing artificial feet equipped with split-hoof-inspired protuberances and testing them under different conditions. These bio-inspired feet demonstrate an anisotropic behavior enabling reduction of sinkage depth up to 46.3%, suction force by 47.6%, and energy cost of stepping on mud by up to 70.4%. Finally, we mounted these artificial feet on a Go1 quadruped robot moving in mud and observed 38.7% reduction of the mechanical cost of transport and 55.0% increase of speed. Those results help us understand the physics of mud locomotion of animals and design better robots moving on wet terrains. We did not find any disadvantages of the split-hooves-inspired design on hard ground, which suggests that redesigning the feet of quadruped robots improves their overall versatility and efficiency on natural terrains.

Granular scaling laws for helically driven dynamics

Exploration of granular physics for three-dimensional geometries interacting with deformable media is crucial for further understanding of granular mechanics and vehicle-terrain dynamics. A modular screw propelled vehicle is, therefore, designed for testing the accuracy of a novel helical granular scaling law in predicting vehicle translational velocity and power. A dimensional analysis is performed on the vehicle and screw pontoons. Two additional pontoon pairs of increased size and mass are determined from dimensional scalars. The power and velocity of these larger pairs are predicted by the smaller pair using the scaling relationships. All three sets are subjected to ten trials of five angular velocities ranging from 13.7 to 75.0 revolutions per minute in a high interlock lunar regolith analog derived from mining tailings. Experimental agreement for prediction of power (3-9% error) and translational velocity (2-12% error) are observed. A similar set of geometries is subjected to multibody dynamics and discrete element method cosimulations of Earth and lunar gravity to verify a gravity-dependent subset of the scaling laws. These simulations show agreement (under 5% error for all sets) and support law validity for gravity between Earth and lunar magnitude. These results support further expansion of granular scaling models to enable prediction for vehicle-terrain dynamics for a variety of environments and geometries.

The effects of reduced-gravity on planetary rover mobility

One of the major challenges faced by planetary exploration rovers today is the negotiation of difficult terrain, such as fine granular regolith commonly found on the Moon and Mars. Current testing methods on Earth fail to account for the effect of reduced gravity on the soil itself. This work characterizes the effects of reduced gravity on wheel–soil interactions between an ExoMars rover wheel prototype and a martian soil simulant aboard parabolic flights producing effective martian and lunar gravitational accelerations. These experiments are the first to collect wheel–soil interaction imagery and force/torque sensor data alongside wheel sinkage data. Results from reduced-gravity flights are compared with on-ground experiments with all parameters equal, including wheel load, such that the only difference between the experiments is the effect of gravity on the soil itself. In lunar gravity, a statistically significant average reduction in traction of 20% is observed compared with 1 g, and in martian gravity an average traction reduction of 5–10% is observed. Subsurface soil imaging shows that soil mobilization increases as gravity decreases, suggesting a deterioration in soil strength, which could be the cause of the reduction in traction. Statistically significant increases in wheel sinkage in both martian and lunar gravity provide additional evidence for decreased soil strength. All of these observations (decreased traction, increased soil mobilization, and increased sinkage) hinder a rover’s ability to drive, and should be considered when interpreting results from reduced-load mobility tests conducted on Earth.

Effective drag of a rod in fluid-saturated granular beds

We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of the depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction μ_{e} encountered over six orders of magnitude of speeds. While a constant μ_{e} is found when the grain size, rod depth, and fluid viscosity are varied at low speeds, a systematic increase is observed as the speed is increased. We analyze μ_{e} in terms of the inertial number I and viscous number J to understand the relative importance of inertia and viscous forces, respectively. For sufficiently high fluid viscosities, we find that the effect of varying the speed, depth, and viscosity can be described by the empirical function μ_{e}=μ_{o}+kJ^{n}, where μ_{o} is the effective friction measured in the quasistatic limit, and k and n are material constants. The drag is then analyzed in terms of the effective viscosity η_{e} and found to decrease systematically as a function of J. We further show that η_{e} as a function of J is directly proportional to the fluid viscosity and the μ_{e} encountered by the rod.

Helically-driven granular mobility and gravity-variant scaling relations

This study discusses the role and function of helical design as it relates to slippage during translation of a vehicle in glass bead media. We show discrete element method (DEM) and multi-body dynamics (MBD) simulations and experiments of a double-helix Archimedes screw propelled vehicle traveling in a bed of soda-lime glass beads. Utilizing granular parameters from the literature and a reduced Young's modulus, we validate the set of granular parameters against experiments. The results suggest that MBD-DEM provides reliable dynamic velocity estimates. We provide the glass, ABS, and glass-ABS simulation parameters used to obtain these results. We also examine recently developed granular scaling laws for wheels applied to these shear-driven vehicles under three different simulated gravities. The results indicate that the system obeys gravity granular scaling laws for constant slip conditions but is limited in each gravity regime when slip begins to increase.