Modeling the locomotion of articulated soft robots in granular medium

Soft robots, in contrast to their rigid counter parts, have infinite degrees of freedom that are coupled with their interaction with the environment. We consider the locomotion of an untethered robot, in the granular medium, comprised of multiple flexible flagella that rotate about an axis by a motor. Drag from the grains causes the flagella to deform and the deformed shape generates a net forward propulsion. This external drag force depends on the shape of the flagella, while the change in flagellar shape is the result of the competition between the external loading and elastic forces. We introduce a numerical tool that couples discrete differential geometry based simulation of elastic rods - our model for flagella - and a resistive force theory based model for the drag. In parallel with simulations, we conduct experiments to quantify the propulsive speed of this class of robots. We find reasonable quantitative agreement between experiments and simulations. Owing to a rod-based kinematic representation of the robot, the simulation runs faster than real-time, and, therefore, we can use it as a design tool for this class of soft robots. We find that there is an optimal rotational speed at which maximum efficiency is achieved. Moreover, both experiments and simulations show that increasing the number of flagella decreases the speed of the robot. We also gain insight into the mechanics of granular medium - while resistive force theory can successfully describe the propulsion at low number of flagella, it fails when more flagella are added to the robot.