Field-mediated locomotor dynamics on highly deformable surfaces

Abstract

In many systems motion occurs on deformed and deformable surfaces, setting up the possibility for dynamical interactions solely mediated by the coupling of the entities with their environment. Here we study the "two-body" dynamics of robot locomotion on a highly deformable spandex membrane in two scenarios: one in which a robot orbits a large central depression and the other where the two robots affect each other's motion solely through mutual environmental deformations. Inspired by the resemblance of the orbits of the single robot with those of general relativistic orbits around black holes, we recast the vehicle plus membrane dynamics in physical space into the geodesic motion of a "test particle" in a fiducial curved space-time and demonstrate how this framework facilitates understanding the observed dynamics. The two-robot problem also exhibits a resemblance with Einstein's general relativistic view of gravity, which in the words of Wheeler: "spacetime tells matter how to move; matter tells spacetime how to curve." We generalize this case the mapping to include a reciprocal coupling that translates into robotic curvature-based control schemes which modify interaction (promoting avoidance or aggregation) without long-range sensing. Our work provides a starting point for developing a mechanical analog gravity system as well as develops a framework that can provide insights into active matter in deformable environments and robot exploration in complex landscapes.

References in corpus (10)

• Novel type of phase transition in a system of self-driven particles
• Non-reciprocal phase transitions
• Phase transition in the collective migration of tissue cells: experiment and model
• Hawking radiation from ultrashort laser pulse filaments
• Low rattling: A predictive principle for self-organization in active collectives
• Geometric visualization of self-propulsion in a complex medium
• Programming Active Cohesive Granular Matter with Mechanically Induced Phase Changes
• Method of image charges for describing linear deformation of bounded 2D solid structures with circular holes and inclusions
• Field-mediated locomotor dynamics on highly deformable surfaces
• Relatively complicated? Using models to teach general relativity at different levels

Cited by in corpus (4)

• Bidirectional Wave-Propelled Capillary Spinners
• Field-mediated locomotor dynamics on highly deformable surfaces
• Locomotion without force, and impulse via dissipation: Robotic swimming in curved space via geometric phase
• A robophysical model of spacetime dynamics