Anyone who’s tried to move through fine sand—whether running along the beach or driving through the desert—knows the difficulty that a loose, granular track presents to locomotion. Now with the aid of a six-legged robot, a team of researchers has determined how much the depth, orientation and direction of a foot, wheel or other means of propulsion affects one’s ability to travel over sand and other types of deformable surfaces.

Many small legged animals—not to mention robots—have difficulty moving on natural substrates such as sand, gravel, rubble, soil, mud, snow, grass and leaf litter, which, unlike solid ground, yield under pressure. The study of "terradynamics"–as opposed to aerodynamics or hydrodynamics—should help engineers and designers better understand how best to traverse such surfaces, the researchers report in the March 22 issue of the journal Science. (pdf)

“Figuring this out is an even more difficult problem than studying movement through fluids,” writes the team, led by physicist Daniel Goldman of the Georgia Institute of Technology. “The complexity of the interactions with such ‘flowable ground’ may rival or even exceed that during movement in fluids.”

Goldman and his colleagues—Chen Li, a postdoctoral fellow at the University of California at Berkeley, and Tingnan Zhang, a graduate student in Goldman's laboratory–3-D printed legs in a variety of shapes for their robot and developed equations for accurately predicting how well each leg type would move the 150-gram, 13-centimeter-long device through different types of granular surfaces [see video below]. Such equations describe and predict that this type of movement could mean the difference between building robots and other vehicles that can travel across virtually any type of terrain and those destined to suffer the same fate as the Mars Exploration Rover Spirit, whose six-year, 7.7-kilometer journey came to an end in late 2009 when its wheels became stuck in a patch of loose Martian soil.

The latest results of this project, which began in 2007, build on earlier experiments. In February 2009, Goldman led a study published in the Proceedings of the National Academy of Sciences (pdf) that described how a robot might best “walk” across granular surfaces. At the time, he and his team built a six-legged, 30-centimeter-long “SandBot”—which weighed 2.3 kilograms—that could adapt to surface changes as it traveled along a 2.4-meter-long track filled with poppy seeds.

Just like Goldman’s current robot, SandBot traveled on six "c-limbs" shaped like apostrophes. One of the main lessons of that experiment was that slowing down the movement of SandBot's limbs allowed the sand to act more like a solid surface. The researchers were able to get SandBot moving along at 30 centimeters per second (still only half as fast as it could move on solid ground).

In both experiments, the convex c-shaped limbs worked much better than straight paddle-like limbs because the former help the robot generate large lift and small body drag, according to the researchers. The straighter legs dug deeper into the sand.