Substrate-mediated interaction of active agents on an elastic membrane

Substrate-mediated interaction is observed in many biological and artificial systems. To discover principles by which collections of active agents can influence each other solely via environmental interaction, we study the dynamics of two robotic vehicles (10 cm in diameter, 150 gram in mass) on a deformable spandex membrane with a radius of 1.2 m; each vehicle’s motion is affected by both the global curvature of the membrane and local deformations due to the other vehicle. The vehicles are driven forward by a motor/differential system which enforces constant (but variable) speed movement; the vehicles turn according to the local slope of membrane. We initiated two vehicles at different locations and orientations on the membrane, monitored the vehicle trajectories, and recorded the time for them to collide (and remain in contact) due to the membrane-mediated coupling. While dynamics and trajectories could be complex, in general, increasing vehicle masses and/or decreasing speeds decreased the merger time. A mathematical model which incorporates the reciprocal interactions captures these dynamics and facilitates design of a controller that avoids collisions by changing a vehicle’s speed as a function of its locally sensed slope.