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

M Casiulis and E Arbel and C van Waes and Y Lahini and S Martiniani and N Oppenheimer and MYB Zion, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 122, e2502211122 (2025).

DOI: 10.1073/pnas.2502211122

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 metamaterials and in embodied decentralized control.

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