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Updated: Jan 18, 2026
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A geometric condition for robot-swarm cohesion and cluster-flock transition
Mathias Casiulis1,2, Eden Arbel3, Charlotte van Waes4
1Center for Soft Matter Research, Department of Physics, New York University, New York, NY 10003.
Summary
We discovered a geometric design rule for controlling particle cluster size. Individual particle properties, like radius and a new parameter called curvity, dictate collective behaviors such as flocking and self-limiting clustering.
Area of Science:
- Physics
- Robotics
- Materials Science
Background:
- Self-propelled particles exhibit complex collective behaviors.
- Controlling particle clustering is crucial for applications like metamaterials.
Purpose of the Study:
- To introduce a geometric design rule for size-controlled clustering of self-propelled particles.
- To define and utilize a new intrinsic parameter, 'curvity', for active particles.
Main Methods:
- Derivation of the 'curvity' parameter from first principles.
- Experimental studies using robots.
- Numerical simulations of particle swarms.
Main Results:
- Curvity, an intrinsic signed parameter, quantifies particle rotational tendency.
- Individual particle radius and curvity control pair cohesion in binary systems.
- These properties govern flocking stability and self-limiting clustering in swarms.
Conclusions:
- The geometric design rule enables precise control over particle cluster size and behavior.
- Curvity is a key factor in predicting and controlling collective dynamics.
- Applications include advanced metamaterials and decentralized robotic control systems.
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