Granular lift forces predict vertical motion of a sand-swimming robot

Previously we modeled the undulatory subsurface locomotion of the sandfish lizard with a sand-swimming robot which displayed performance comparable to the organism. In this work we control the lift forces on the robot by varying its head shape and demonstrate that these granular forces predict the vertical motion of the robot. Inspired by the tapered head of the sandfish lizard, we drag a wedge shaped object horizontally and parallel to its lower face through a granular medium and show that by varying the angle of the upper leading surface of the wedge, α, the lift force can be varied from positive to negative. Testing the robot with these wedges as heads results in vertical motion in the same direction as the lift force in the drag experiments. As the robot moves forward, the force on its head normal to the body plane results in a net torque imbalance which pitches the robot causing it to rise or sink within the medium. Since repeatedly varying α for a wedge head to achieve a desired lift is impractical, we test robot heads that approximate a wedge head inclined at varying angles by changing the angle of the bottom and top surfaces of the wedge, and show that similar lift control is achieved. Our results provide principles for the construction of robots that will be able to follow arbitrary trajectories within complex substrates like sand, and also lend support to hypotheses that morphological adaptations of desert-dwelling organisms aid in their subsurface locomotion.