A geometric condition for robot-swarm cohesion and cluster–flock transition - Mathias Casiulis; Eden Arbel; Charlotte van Waes; Yoav Lahini; Stefano Martiniani; Naomi Oppenheimer; Matan Yah Ben Zion (Proceedings of the National Academy of Sciences, 2025)
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.