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

M Mathias Casiulis (Center for Soft Matter Research, Department of Physics, New York University) E Eden Arbel (Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University) C Charlotte van Waes (Department of Artificial Intelligence, Donders Center for Cognition, Radboud University) Y Yoav Lahini (Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University) S Stefano Martiniani (Center for Soft Matter Research, Department of Physics, New York University) N Naomi Oppenheimer (Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University) M Matan Yah Ben Zion (Department of Artificial Intelligence, Donders Center for Cognition, Radboud University)

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 metamaterials and in embodied decentralized control.

Article Details

Volume / Issue Vol. 122, Issue 37
Published September 16, 2025
ISSN 0027-8424
Publisher National Academy of Sciences

Authors (7)

M

Mathias Casiulis

Center for Soft Matter Research, Department of Physics, New York University

E

Eden Arbel

Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University

C

Charlotte van Waes

Department of Artificial Intelligence, Donders Center for Cognition, Radboud University

Y

Yoav Lahini

Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University

S

Stefano Martiniani

Center for Soft Matter Research, Department of Physics, New York University

N

Naomi Oppenheimer

Department of Condensed Matter Physics, School of Physics and Astronomy, Center for Physics, Chemistry of Living Systems, Tel Aviv University

M

Matan Yah Ben Zion

Department of Artificial Intelligence, Donders Center for Cognition, Radboud University