Modeling of elastically coupled robots locomoting on an elastic membrane

Based on previous work (Li et al., PNAS, 2022) involving a single two-wheeled robot (diameter 10 cm) locomoting on a deformable spandex membrane (diameter 2.4 m) we seek to model the rich dynamics of a modified system composed of two disk-shaped robots connected by a linear spring. Experiments reveal that the elastically connected vehicles can be captured in a trajectory where one vehicle always remains closer to a central depression. These “tidally-locked” dynamics are influenced by the coupling of the vehicles to their environment, their coupling to each other via the spring, and the interaction of the deformations they create in the membrane. To gain insight into the dynamics, we develop a numerical model with several important features. First, the model incorporates each vehicle’s differential drive which allows the wheels to have different drive forces, but enforces the constraint that the sum of the wheels’ drive forces remains constant. The interaction between the wheels and the elastic membrane is modeled by using experimentally measured drag forces on a constant speed wheel moving across the membrane at varying attack angles. We couple the vehicles to the environment using a measured mapping from membrane radius to centripetal force. The force between the vehicles is modeled as linear in the distance between robots. We find that the trajectories created by this model qualitatively match those seen in experiment and provide insights into the mechanism governing robophysical tidal locking.