Helical locomotion in a granular medium by a 'sand robot'
Moving within granular media such as sand is a trick that occurs not only in science-fiction movies. The sandfish lizard, which lives in the desert, is also able to perform this task. In order to do so, this lizard behaves as a fish and undulates its body to reach a top speed of two body lengths per second.
The propulsion of sandfish lizards has been proved to result from the fact that the resistance into sand is larger for a motion in a direction perpendicular to the body than for a motion in a longitudinal direction. Such a property is called anisotropic friction.
Far from deserts and granular media, other organisms use such anisotropic properties of the media in order to propel themselves. This is the case for micro-organisms in viscous fluids. Like in sand, their bodies experience a resistance per body length which is larger for a perpendicular motion than for a longitudinal one. This explains why many bacteria undulate their tails in order to propel in viscous fluids like sandfish in sand.
However, beating a tail is not the only mode of locomotion employed by bacteria to move in a viscous fluid. For example, E. coli use the rotation of a helical tail for the same purpose.
Such an observation has raised the curiosity of a team of researchers at the Physics Department of the University of Santiago in Chile. Francisco Melo, who leads the team, asked himself: "Does helical rotation induce propulsion into a granular media as in a viscous fluid?"
In order to answer the question, Alejandro Ibarra, a Ph.D. student involved in this project, imagined an experiment to study the horizontal motion of a helix rotating into a granular medium. The researchers placed a helix in a pool of grains and connected it to an external motor by the way of a small rod passing through the wall of the pool. The motor was located onto a linear stage to permit its horizontal motion. This setup allows the rotation of the helix while freeing its horizontal motion.
"We observed that when the helix was sufficiently deep into the granular medium, its rotation led to a propulsive motion along the horizontal axis," said Baptiste Darbois Texier, a postdoctoral researcher at the Physics Department.
With this setup, the researchers studied the velocity of the helix depending on its rotation speed, its depth into the granular pool and the external load applied to the system. Moreover, they fabricated helices of different geometries and tested them in the granular pool. In parallel, they developed a theoretical model to describe the anisotropic friction experienced by the helix based on a longitudinal and transversal friction coefficient. The model captures their experimental observations and predicts the optimal design of the helix in order to propel in a granular medium.
Finally, the team developed a proof-of-concept robot based on helical propulsion that operates in granular material. The robot head contains a small battery and a tiny motor that ensures the rotation of the helical tail. The design also includes four pallets in order to avoid the rotation of the head rather than the tail. The robot proved to be very robust in propelling through different types of grains. Because the actuation of this sand robot is based on a simple motor, it is much easier to implement than those reproducing the undulating motion of sandfish lizards. Thus, this study paves the way to a new kind of robot operating in heterogeneous media such as sand or dry snow.