Field-mediated locomotor dynamics on highly deformable surfaces

Robophysical modeling of spacetime dynamics

“…We further reasoned that the programmability and sensory capabilities of increasingly low-cost and powerful "robophysical" models [4,5] could allow tuning of parameters that lead to inexact mimics of GR in passive systems. Indeed, our recent work [6] built a framework to understand how the field-mediated dynamics of active agents on flexible membranes demonstrate in the words of Wheeler's famous aphorism: "matter tells spacetime how to curve and spacetime tells matter how to move" [7]. In particular, we show that the spacetime followed by an active object can be tuned by varying system parameters such as the membrane elasticity and the speed of the object.…”

“…Here we amplify on and extend the scheme introduced in [6] and demonstrate how the activity can lead to an exact mapping to GR. We first show how an active object with prescribed speed on an elastic membrane produces longer and more controllable trajectories compared with a passive marble.…”

“…To understand these orbits, we follow the models in [6,8]. While a passive marble dissipates energy as a• v < 0 (Fig.…”

“…On the other hand, when v is finite and controllable, the active locomotion provides more flexibility and programmability in fabricating the desired spacetime depicted by GR than the passive agents studied in the previous works such as the dissipative marbles [1,8] rolling on a membrane. For instance, the conserved quantity directly led from the metric could show that a k increasing with r makes an orbit have a precession with a sign opposite to the orbit while a k decreasing with r makes an orbit have a precession with a sign same as the orbit [6].…”

“…Beyond its role as a mechanical analog for GR, this framework could also provide a new perspective to understand active matter undergoing field-mediated interactions [6,22]. For instance, the spacetime metric of the agents' motion can both guide our choice of parameter values to alter orbital features like the precession sign and influence our design of control schemes that accomplish tasks like helping multiple agents avoid mergers on the membrane [6].…”