A geometric condition for robot-swarm cohesion and cluster-flock transition

TL;DR

This paper introduces a geometric design rule based on a curvature parameter called curvity, which predicts and controls clustering and flocking behavior in robot swarms and active particles.

Contribution

It defines a new intrinsic signed curvature parameter, curvity, derived from first principles, to predict and control clustering and flocking in active particle systems.

Findings

Curvity determines pair cohesion in binary systems.

Robot properties influence swarm stability and clustering.

Experimental and simulation results validate the geometric design rule.

Abstract

We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we call curvity, that can be derived from first principles. Experiments with robots and numerical simulations show that properties of individual robots (radius and curvity) control pair cohesion in a binary system, and the stability of flocking and self-limiting clustering in a swarm, with applications in meta-materials and in embodied decentralized control.