Robotic swarms are groups of robots that work together to handle tough jobs like exploring, collecting items, or moving things. To work on a large scale, these swarms can’t depend on a central controller or complicated programming. Instead, they need simple rules that let complex group behavior naturally emerge.
In a recent study, scientists from institutions including Radboud University and New York University unveiled a new framework to improve swarm intelligence, the kind of group coordination seen in birds flocking or fish schooling.
Instead of relying on complex programming or central control, the team developed simple geometric rules that mimic natural forces. Each robot is given a property called “curvity”, similar to electric charge, which determines how it moves and interacts with others. This helps the swarm decide whether to flock, flow, or cluster.
Scientists ran experiments showing that a simple rule based on “curvity” can guide how robots interact. Each robot was given a positive or negative curvity, like an electric charge, which determined whether it was attracted to or repelled by others. This rule worked not just for pairs, but scaled up to thousands of robots, helping the whole swarm move and organize itself naturally.

Ben Zion, who as an NYU student previously developed microscopic swimmers, added, “This charge-like quantity, which we call ‘curvity,’ can take positive or negative values and can be directly encoded into the mechanical structure of the robot. As with particle charges, the value of the curvity determines how robots become attracted to one another to cluster or deflect from one another to flock.”
“Finding a design rule of geometric nature, such as curvature, makes it applicable to industrial or delivery robots or to cellular-sized microscopic robots that have the potential to improve drug delivery and other medical treatments.”
“The best part is that these rules are based on elementary mechanics, making their implementation in a physical robot straightforward,” adds Casiulis, a postdoctoral researcher at New York University’s Center for Soft Matter Research and NYU’s Simons Center for Computational Physical Chemistry. “More broadly, this work transforms the challenge of controlling swarms into an exercise in material science, offering a simple design rule to inform future swarm engineering.”
Journal Reference:
- Mathias Casiulis, Eden Arbel et al. A geometric condition for robot-swarm cohesion and cluster–flock transition. Proceedings of the National Academy of Sciences. DOI: 10.1073/pnas.2502211122